Project Euler

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54

In Python

In C++

#1: Multiples of 3 and 5

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

function opdracht1(limit = 1000) { function summation(n, xmax) { var xlen = xmax / n |0; return Math.floor((xlen * (xlen + 1)) / 2) * n; } return summation(3, limit - 1) + summation(5, limit - 1) - summation(15, limit - 1); } alert(opdracht1()); // should give 233,168

#2: Even Fibonacci numbers

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

function opdracht2() { var xmax = 4*10**6, term1 = 1, term2 = 2, temp = 0, xsum = 2; while ((temp = term1 + term2) <= xmax) { if (temp % 2 == 0) xsum += temp; term1 = term2, term2 = temp; } return xsum; } alert(opdracht2()); // should give 4,613,732

#3: Largest prime factor

The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600,851,475,143?

function opdracht3() { function primefactors(n) { var primes = [], factors = []; function primefactor(primes, n = 13195) { function appendprime(primes) { if (primes.length < 1) primes.push(2); if (primes.length < 2) primes.push(3); var p = primes[primes.length - 1] + 2; for (var i = 2; i < p; i++) if (p % i == 0) p++, i = 1; primes.push(p); return primes; } for (var i = 0; true; i++) { if (primes.length <= i) appendprime(primes); if (n % primes[i] == 0) return primes[i]; } } while (true) { var factor = primefactor(primes, n); factors.push(factor); if (factor == n) break; n = Math.floor(n / factor); } return factors } return Math.max.apply(null, primefactors(600851475143)); } alert(opdracht3()); // should be 6,857

#4: Largest palindrome product

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 x 99.

Find the largest palindrome made from the product of two 3-digit numbers.

function opdracht4() { function ispalindrome(n) { var temp = n, rev = 0; while (temp != 0) rev = rev * 10 + temp % 10, temp = Math.floor(temp / 10); return n == rev; } var best = 0; for (var a = 100; a < 1000; a++) { for (var b = 100; b < 1000; b++) { var c = a * b; if (ispalindrome(c) && c > best) best = c; } } return best; } alert(opdracht4()); // should be 906,609

#5: Smallest multiple

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.

What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

function opdracht5() { function isdivisible(n, l) { for (var i = 0; i < l.length; i++) if (n % l[i] > 0) return 0; return 1; } var start = 2520, number = start; while (isdivisible(number, [11,12,13,14,15,16,17,18,19,20]) == 0) number += start; return number; } alert(opdracht5()); // shouuld give 232,792,560

#6: Sum square difference

The sum of the squares of the first ten natural numbers is, 1^2 + 2^2 + ... + 10^2 = 385

The square of the sum of the first ten natural numbers is, (1 + 2 + ... + 10)2 = 552 = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 - 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

function opdracht6() { var sumsquare = 0, squaresum = 0; for (var x = 1; x <= 100; x++) sumsquare += x**2, squaresum += x; return squaresum ** 2 - sumsquare; } alert(opdracht6()); // should give 25,164,150

#7: 10001st prime

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

What is the 10 001st prime number?

function opdracht7() { function reducer(n, presets = [300, 100, 8]) { for (var i = 0; i < presets.length; i++) if (n > presets[i] * presets[i]) return n / presets[i] |0; return n; } var p = 3, sqp = reducer(p), ret = 0, n = 10001; for (var j = 0; j < n - 1; j++) { for (var i = 2; i < sqp; i++) if (p % i == 0) sqp = reducer(++p), i = 1; ret = p, p += 2, sqp = reducer(p); } return ret; } alert(opdracht7()); // should give 104,743

#8 Largest product in a series

The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832. 

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?

series8 = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450"; function opdracht8(series1 = series8) { var best = 0; for (var i = 0; i < series1.length - 13; i++) { var product = 1; for (var j = 0; j < 13; j++) product *= series1[i + j]; best = Math.max(best, product); } return best; } alert(opdracht8()); // should give 23,514,624,000

#9 Special Pythagorean triplet

A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a2 + b2 = c2

For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.

There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.

function opdracht9(search = 1000) { for (var a = 1; a < search - 1; a++) { for (var b = 1; b < search - a; b++) { var c = search - a - b; if (a * a + b * b == c * c) return a * b * c; } } return 0; } alert(opdracht9()); // should give 31,875,000

#10 Summation of primes

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

Find the sum of all the primes below two million.

function opdracht10(limit = 2*10**6) { var v = Array(limit).fill(true); v[0] = v[1] = false; for (var p = 2; p * p < v.length; p++) if (v[p] == true) for (i = p * 2; i <= v.length; i += p) v[i] = false; var sum = 0; for (var i = 0; i < v.length; i++) sum += v[i] == true ? i : 0; return sum; } alert(opdracht10()); // should give 142,913,828,922

#11 Largest product in a grid

In the 20×20 grid below, four numbers along a diagonal line have been marked in red. 

08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48

The product of these numbers is 26 × 63 × 78 × 14 = 1788696.

What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?

t11 = [[ 8, 2,22,97,38,15, 0,40, 0,75, 4, 5, 7,78,52,12,50,77,91, 8], [49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48, 4,56,62, 0], [81,49,31,73,55,79,14,29,93,71,40,67,53,88,30, 3,49,13,36,65], [52,70,95,23, 4,60,11,42,69,24,68,56, 1,32,56,71,37, 2,36,91], [22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80], [24,47,32,60,99, 3,45, 2,44,75,33,53,78,36,84,20,35,17,12,50], [32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70], [67,26,20,68, 2,62,12,20,95,63,94,39,63, 8,40,91,66,49,94,21], [24,55,58, 5,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72], [21,36,23, 9,75, 0,76,44,20,45,35,14, 0,61,33,97,34,31,33,95], [78,17,53,28,22,75,31,67,15,94, 3,80, 4,62,16,14, 9,53,56,92], [16,39, 5,42,96,35,31,47,55,58,88,24, 0,17,54,24,36,29,85,57], [86,56, 0,48,35,71,89, 7, 5,44,44,37,44,60,21,58,51,54,17,58], [19,80,81,68, 5,94,47,69,28,73,92,13,86,52,17,77, 4,89,55,40], [ 4,52, 8,83,97,35,99,16, 7,97,57,32,16,26,26,79,33,27,98,66], [88,36,68,87,57,62,20,72, 3,46,33,67,46,55,12,32,63,93,53,69], [ 4,42,16,73,38,25,39,11,24,94,72,18, 8,46,29,32,40,62,76,36], [20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74, 4,36,16], [20,73,35,29,78,31,90, 1,74,31,49,71,48,86,81,16,23,57, 5,54], [ 1,70,54,71,83,51,54,69,16,92,33,48,61,43,52, 1,89,19,67,48]]; function opdracht11(data = t11) { var best = 0; for (var i = 0; i < 20; i++) { for (var j = 0; j < 16; j++) { var prod = data[i][j] * data[i][j+1] * data[i][j+2] * data[i][j+3]; best = Math.max(prod, best); prod = data[j][i] * data[j+1][i] * data[j+2][i] * data[j+3][i]; best = Math.max(prod, best); } } for (var i = 0; i < 16; i++) { for (var j = 0; j < 16; j++) { var prod = data[i][j] * data[i+1][j+1] * data[i+2][j+2] * data[i+3][j+3]; best = Math.max(prod, best); } } for (var i = 3; i < 20; i++) { for (var j = 0; j < 16; j++) { var prod = data[i][j] * data[i-1][j+1] * data[i-2][j+2] * data[i-3][j+3]; best = Math.max(prod, best); } } return best; } alert(opdracht11()); // should give 70,600,674

#12 Highly divisible triangular number

The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

Let us list the factors of the first seven triangle numbers: 

     1: 1
     3: 1,3
     6: 1,2,3,6
    10: 1,2,5,10
    15: 1,3,5,15
    21: 1,3,7,21
    28: 1,2,4,7,14,28

We can see that 28 is the first triangle number to have over five divisors.

What is the value of the first triangle number to have over five hundred divisors?

function opdracht12(divisors = 500) { function triangler(n) { return n * (n + 1) >> 1; } function n_divs(n) { if (n % 2 == 0) n = n >> 1; var divisors = 1, count = 0; while (n % 2 == 0) count++, n = n >> 1; divisors = divisors * (count + 1); for (var p = 3; n != 1; p += 2) { count = 0; while (n % p == 0) count++, n = Math.floor(n / p); divisors = divisors * (count + 1); } return divisors; } function find_triangular_index(factor_limit = 500) { var n = 1; for (var lnum = n_divs(n), rnum = n_divs(n + 1); lnum * rnum < factor_limit;) ++n, lnum = rnum, rnum = n_divs(n + 1); return n; } var index = find_triangular_index(divisors); return triangler(index); } alert(opdracht12()); // should give 76,576,500

#13 Large sum

Work out the first ten digits of the sum of the following one-hundred 50-digit numbers. 

37107287533902102798797998220837590246510135740250
46376937677490009712648124896970078050417018260538
74324986199524741059474233309513058123726617309629
91942213363574161572522430563301811072406154908250
23067588207539346171171980310421047513778063246676
89261670696623633820136378418383684178734361726757
28112879812849979408065481931592621691275889832738
44274228917432520321923589422876796487670272189318
47451445736001306439091167216856844588711603153276
70386486105843025439939619828917593665686757934951
62176457141856560629502157223196586755079324193331
64906352462741904929101432445813822663347944758178
92575867718337217661963751590579239728245598838407
58203565325359399008402633568948830189458628227828
80181199384826282014278194139940567587151170094390
35398664372827112653829987240784473053190104293586
86515506006295864861532075273371959191420517255829
71693888707715466499115593487603532921714970056938
54370070576826684624621495650076471787294438377604
53282654108756828443191190634694037855217779295145
36123272525000296071075082563815656710885258350721
45876576172410976447339110607218265236877223636045
17423706905851860660448207621209813287860733969412
81142660418086830619328460811191061556940512689692
51934325451728388641918047049293215058642563049483
62467221648435076201727918039944693004732956340691
15732444386908125794514089057706229429197107928209
55037687525678773091862540744969844508330393682126
18336384825330154686196124348767681297534375946515
80386287592878490201521685554828717201219257766954
78182833757993103614740356856449095527097864797581
16726320100436897842553539920931837441497806860984
48403098129077791799088218795327364475675590848030
87086987551392711854517078544161852424320693150332
59959406895756536782107074926966537676326235447210
69793950679652694742597709739166693763042633987085
41052684708299085211399427365734116182760315001271
65378607361501080857009149939512557028198746004375
35829035317434717326932123578154982629742552737307
94953759765105305946966067683156574377167401875275
88902802571733229619176668713819931811048770190271
25267680276078003013678680992525463401061632866526
36270218540497705585629946580636237993140746255962
24074486908231174977792365466257246923322810917141
91430288197103288597806669760892938638285025333403
34413065578016127815921815005561868836468420090470
23053081172816430487623791969842487255036638784583
11487696932154902810424020138335124462181441773470
63783299490636259666498587618221225225512486764533
67720186971698544312419572409913959008952310058822
95548255300263520781532296796249481641953868218774
76085327132285723110424803456124867697064507995236
37774242535411291684276865538926205024910326572967
23701913275725675285653248258265463092207058596522
29798860272258331913126375147341994889534765745501
18495701454879288984856827726077713721403798879715
38298203783031473527721580348144513491373226651381
34829543829199918180278916522431027392251122869539
40957953066405232632538044100059654939159879593635
29746152185502371307642255121183693803580388584903
41698116222072977186158236678424689157993532961922
62467957194401269043877107275048102390895523597457
23189706772547915061505504953922979530901129967519
86188088225875314529584099251203829009407770775672
11306739708304724483816533873502340845647058077308
82959174767140363198008187129011875491310547126581
97623331044818386269515456334926366572897563400500
42846280183517070527831839425882145521227251250327
55121603546981200581762165212827652751691296897789
32238195734329339946437501907836945765883352399886
75506164965184775180738168837861091527357929701337
62177842752192623401942399639168044983993173312731
32924185707147349566916674687634660915035914677504
99518671430235219628894890102423325116913619626622
73267460800591547471830798392868535206946944540724
76841822524674417161514036427982273348055556214818
97142617910342598647204516893989422179826088076852
87783646182799346313767754307809363333018982642090
10848802521674670883215120185883543223812876952786
71329612474782464538636993009049310363619763878039
62184073572399794223406235393808339651327408011116
66627891981488087797941876876144230030984490851411
60661826293682836764744779239180335110989069790714
85786944089552990653640447425576083659976645795096
66024396409905389607120198219976047599490197230297
64913982680032973156037120041377903785566085089252
16730939319872750275468906903707539413042652315011
94809377245048795150954100921645863754710598436791
78639167021187492431995700641917969777599028300699
15368713711936614952811305876380278410754449733078
40789923115535562561142322423255033685442488917353
44889911501440648020369068063960672322193204149535
41503128880339536053299340368006977710650566631954
81234880673210146739058568557934581403627822703280
82616570773948327592232845941706525094512325230608
22918802058777319719839450180888072429661980811197
77158542502016545090413245809786882778948721859617
72107838435069186155435662884062257473692284509516
20849603980134001723930671666823555245252804609722
53503534226472524250874054075591789781264330331690
digits13 = ["37107287533902102798797998220837590246510135740250", "46376937677490009712648124896970078050417018260538", "74324986199524741059474233309513058123726617309629", "91942213363574161572522430563301811072406154908250", "23067588207539346171171980310421047513778063246676", "89261670696623633820136378418383684178734361726757", "28112879812849979408065481931592621691275889832738", "44274228917432520321923589422876796487670272189318", "47451445736001306439091167216856844588711603153276", "70386486105843025439939619828917593665686757934951", "62176457141856560629502157223196586755079324193331", "64906352462741904929101432445813822663347944758178", "92575867718337217661963751590579239728245598838407", "58203565325359399008402633568948830189458628227828", "80181199384826282014278194139940567587151170094390", "35398664372827112653829987240784473053190104293586", "86515506006295864861532075273371959191420517255829", "71693888707715466499115593487603532921714970056938", "54370070576826684624621495650076471787294438377604", "53282654108756828443191190634694037855217779295145", "36123272525000296071075082563815656710885258350721", "45876576172410976447339110607218265236877223636045", "17423706905851860660448207621209813287860733969412", "81142660418086830619328460811191061556940512689692", "51934325451728388641918047049293215058642563049483", "62467221648435076201727918039944693004732956340691", "15732444386908125794514089057706229429197107928209", "55037687525678773091862540744969844508330393682126", "18336384825330154686196124348767681297534375946515", "80386287592878490201521685554828717201219257766954", "78182833757993103614740356856449095527097864797581", "16726320100436897842553539920931837441497806860984", "48403098129077791799088218795327364475675590848030", "87086987551392711854517078544161852424320693150332", "59959406895756536782107074926966537676326235447210", "69793950679652694742597709739166693763042633987085", "41052684708299085211399427365734116182760315001271", "65378607361501080857009149939512557028198746004375", "35829035317434717326932123578154982629742552737307", "94953759765105305946966067683156574377167401875275", "88902802571733229619176668713819931811048770190271", "25267680276078003013678680992525463401061632866526", "36270218540497705585629946580636237993140746255962", "24074486908231174977792365466257246923322810917141", "91430288197103288597806669760892938638285025333403", "34413065578016127815921815005561868836468420090470", "23053081172816430487623791969842487255036638784583", "11487696932154902810424020138335124462181441773470", "63783299490636259666498587618221225225512486764533", "67720186971698544312419572409913959008952310058822", "95548255300263520781532296796249481641953868218774", "76085327132285723110424803456124867697064507995236", "37774242535411291684276865538926205024910326572967", "23701913275725675285653248258265463092207058596522", "29798860272258331913126375147341994889534765745501", "18495701454879288984856827726077713721403798879715", "38298203783031473527721580348144513491373226651381", "34829543829199918180278916522431027392251122869539", "40957953066405232632538044100059654939159879593635", "29746152185502371307642255121183693803580388584903", "41698116222072977186158236678424689157993532961922", "62467957194401269043877107275048102390895523597457", "23189706772547915061505504953922979530901129967519", "86188088225875314529584099251203829009407770775672", "11306739708304724483816533873502340845647058077308", "82959174767140363198008187129011875491310547126581", "97623331044818386269515456334926366572897563400500", "42846280183517070527831839425882145521227251250327", "55121603546981200581762165212827652751691296897789", "32238195734329339946437501907836945765883352399886", "75506164965184775180738168837861091527357929701337", "62177842752192623401942399639168044983993173312731", "32924185707147349566916674687634660915035914677504", "99518671430235219628894890102423325116913619626622", "73267460800591547471830798392868535206946944540724", "76841822524674417161514036427982273348055556214818", "97142617910342598647204516893989422179826088076852", "87783646182799346313767754307809363333018982642090", "10848802521674670883215120185883543223812876952786", "71329612474782464538636993009049310363619763878039", "62184073572399794223406235393808339651327408011116", "66627891981488087797941876876144230030984490851411", "60661826293682836764744779239180335110989069790714", "85786944089552990653640447425576083659976645795096", "66024396409905389607120198219976047599490197230297", "64913982680032973156037120041377903785566085089252", "16730939319872750275468906903707539413042652315011", "94809377245048795150954100921645863754710598436791", "78639167021187492431995700641917969777599028300699", "15368713711936614952811305876380278410754449733078", "40789923115535562561142322423255033685442488917353", "44889911501440648020369068063960672322193204149535", "41503128880339536053299340368006977710650566631954", "81234880673210146739058568557934581403627822703280", "82616570773948327592232845941706525094512325230608", "22918802058777319719839450180888072429661980811197", "77158542502016545090413245809786882778948721859617", "72107838435069186155435662884062257473692284509516", "20849603980134001723930671666823555245252804609722", "53503534226472524250874054075591789781264330331690"]; function opdracht13(l = digits13) { var totalSum = [], sum = 0; for (var i = 50; i > 0; i--) { for (var j = 0; j < l.length; j++) sum += l[j].charCodeAt(i - 1) - 48; totalSum.push(sum % 10); sum = Math.floor(sum / 10); } while (sum > 0) { totalSum.push(sum % 10); sum = Math.floor(sum / 10); } var start = totalSum.length - 10; for (var i = 0; i < 10; i++) sum += totalSum[start + i] * 10**i; return sum; } alert(opdracht13()); // should give 5,537,376,230

#14 Longest Collatz sequence

The following iterative sequence is defined for the set of positive integers: n → n/2 (n is even) n → 3n + 1 (n is odd) Using the rule above and starting with 13, we generate the following sequence: 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1 It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1. Which starting number, under one million, produces the longest chain? NOTE: Once the chain starts the terms are allowed to go above one million.

function opdracht14(limit = 10**6) { function collatz(lut, num) { var count = 1, n = num; dict = {}; while (n > 1) { if (lut.length >= n && lut[n - 1] > 0) { count += lut[n - 1] - 1; break; } n = n % 2 == 0 ? Math.floor(n / 2) : n * 3 + 1, count++; // can't do n >> 1 because of 32bit limit } lut[num - 1] = count; return count; } var lut = Array(limit - 1).fill(0), best_start = 0, best_length = 0; for (var i = 1; i < limit; i++) { var len = collatz(lut, i); if (len > best_length) best_start = i, best_length = len; } return best_start; } alert(opdracht14()); // should give 837,799

#15: Lattice paths

Starting in the top left corner of a 2x2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

How many such routes are there through a 20x20 grid?

function opdracht15() { var paths = 1, size = 20; for (var i = 0; i < size; i++) paths = Math.floor((paths * (2 * size - i)) / (i + 1)); return paths; } alert(opdracht15()); // should give 137,846,528,820

#16 Power digit sum

2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.

What is the sum of the digits of the number 2^1000?

function opdracht16(e = 1000) { var largeNum = Array(400).fill(0); largeNum[0] = 2; var carry = 0, sum = 0; while (--e) { for (var i = 0; i < largeNum.length; i++) { largeNum[i] *= 2; largeNum[i] += carry; carry = Math.floor(largeNum[i] / 10); largeNum[i] = largeNum[i] % 10; } } for (var i = 0; i < largeNum.length; i++) sum += largeNum[i]; return sum; } alert(opdracht16()); // should give 1,366

#17 Number letter counts

If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total.

If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would be used?

NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and forty-two) contains 23 letters and 115 (one hundred and fifteen) contains 20 letters. The use of "and" when writing out numbers is in compliance with British usage.

function opdracht17() { var arr = ["one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten", "eleven", "twelve", "thirteen", "fourteen", "fifteen", "sixteen", "seventeen", "eighteen", "nineteen", "twenty", "thirty", "forty", "fifty", "sixty", "seventy", "eighty", "ninety"]; var xsum = 0; for (var i = 0; i < 19; i++) xsum += arr[i].length; for (var i = 19; i < 27; i++) { xsum += arr[i].length; for (var j = 0; j < 9; j++) xsum += arr[i].length + arr[j].length; } for (var i = 0; i < 9; i++) { xsum += arr[i].length + "hundred".length; for (var j = 0; j < 19; j++) xsum += arr[i].length + "hundred".length + "and".length + arr[j].length; for (var j = 19; j < 27; j++) { xsum += arr[i].length + "hundred".length + "and".length + arr[j].length; for (var k = 0; k < 9; k++) xsum += arr[i].length + "hundredand".length + arr[j].length + arr[k].length; } } xsum += "onethousand".length; return xsum; } alert(opdracht17()); // should give 21,124

#18: Maximum path sum I

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. 

3
7 4
2 4 6
8 5 9 3

That is, 3 + 7 + 4 + 9 = 23.

Find the maximum total from top to bottom of the triangle below: 

75
95 64
17 47 82
18 35 87 10
20 04 82 47 65
19 01 23 75 03 34
88 02 77 73 07 63 67
99 65 04 28 06 16 70 92
41 41 26 56 83 40 80 70 33
41 48 72 33 47 32 37 16 94 29
53 71 44 65 25 43 91 52 97 51 14
70 11 33 28 77 73 17 78 39 68 17 57
91 71 52 38 17 14 91 43 58 50 27 29 48
63 66 04 68 89 53 67 30 73 16 69 87 40 31
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23

NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)

triangle18 = [ [75, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [95,64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [17,47,82, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [18,35,87,10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [20, 4,82,47,65, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [19, 1,23,75, 3,34, 0, 0, 0, 0, 0, 0, 0, 0, 0], [88, 2,77,73, 7,63,67, 0, 0, 0, 0, 0, 0, 0, 0], [99,65, 4,28, 6,16,70,92, 0, 0, 0, 0, 0, 0, 0], [41,41,26,56,83,40,80,70,33, 0, 0, 0, 0, 0, 0], [41,48,72,33,47,32,37,16,94,29, 0, 0, 0, 0, 0], [53,71,44,65,25,43,91,52,97,51,14, 0, 0, 0, 0], [70,11,33,28,77,73,17,78,39,68,17,57, 0, 0, 0], [91,71,52,38,17,14,91,43,58,50,27,29,48, 0, 0], [63,66, 4,68,89,53,67,30,73,16,69,87,40,31, 0], [ 4,62,98,27,23, 9,70,98,73,93,38,53,60, 4,23]]; function opdracht18(triangle = triangle18) { var root = triangle[0].length; var possibilities = 2**(root - 1); var best = 0; for (var i = 0; i <= possibilities; i++) { var index = 0, xsum = triangle[0][0]; for (var j = 0; j < root - 1; j++) { index = index + (i >> j & 1); value = triangle[j + 1][index]; xsum += value; } best = Math.max(best, xsum); } return best; } alert(opdracht18()); // should give 1,074

#19 Counting Sundays

You are given the following information, but you may prefer to do some research for yourself.

How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)?

function opdracht19() { function isLeap(year) { if (year % 4 > 0) return false; if (year % 100 > 0) return true; return false; } var months = [31,28,31,30,31,30,31,31,30,31,30,31]; var days = ["Tuesday","Wednesday","Thursday",'Friday','Saturday', 'Sunday', 'Monday']; var day = 0, sunday_count = 0; for (var year = 1901; year <=2000; year++) { var leap = isLeap(year); for (var m = 0; m < months.length; m++) { var dayName = days[day % 7]; if (dayName == "Sunday") sunday_count++; day += months[m]; if (leap == true && months[m] == 28) day++; } } return sunday_count; } alert(opdracht19()); // should give 171

#20 Factorial digit sum

n! means n × (n − 1) × ... × 3 × 2 × 1 For example, 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800, and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27. Find the sum of the digits in the number 100!

function opdracht20(f = 100) { var buf = Array(200).fill(0); buf[0] = f; for (var i = f - 1; i > 0; i--) { var carry = 0; for (var j = 0; j < 200; j++) { buf[j] *= i; buf[j] += carry; carry = Math.floor(buf[j] / 10); buf[j] = buf[j] % 10; } } var sum = 0; for (var i = 0; i < 200; i++) sum += buf[i]; return sum; } alert(opdracht20()); // should give 648

#21 Amicable numbers

Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n). If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers. For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220. Evaluate the sum of all the amicable numbers under 10000.

function amicablePairsSum(low = 1, high = 10**4) { function sumDivisors(n) { var som = 0; for (var i = 1; i < n; i++) if (n % i == 0) som += i; return som; } var l = Array(high - low).fill(0); for (var i = low; i <= high; i++) l[i - low] = sumDivisors(i); var som = 0; for (var i = 0; i <= (high - low); i++) { var ind = l[i]; if (i + low < ind && low <= ind && ind <= high && l[ind - low] == i + low) { som += (i + low) + ind; } } return som; } alert(amicablePairsSum()); // should give 31,626

#22 Names scores

Using names.txt (right click and 'Save Link/Target As...'), a 46K text file containing over five-thousand first names, begin by sorting it into alphabetical order. Then working out the alphabetical value for each name, multiply this value by its alphabetical position in the list to obtain a name score.

For example, when the list is sorted into alphabetical order, COLIN, which is worth 3 + 15 + 12 + 9 + 14 = 53, is the 938th name in the list. So, COLIN would obtain a score of 938 × 53 = 49714.

What is the total of all the name scores in the file?

names22 = ["MARY","PATRICIA","LINDA","BARBARA","ELIZABETH","JENNIFER","MARIA","SUSAN", "MARGARET","DOROTHY","LISA","NANCY","KAREN","BETTY","HELEN","SANDRA","DONNA", "CAROL","RUTH","SHARON","MICHELLE","LAURA","SARAH","KIMBERLY","DEBORAH", "JESSICA","SHIRLEY","CYNTHIA","ANGELA","MELISSA","BRENDA","AMY","ANNA", "REBECCA","VIRGINIA","KATHLEEN","PAMELA","MARTHA","DEBRA","AMANDA", "STEPHANIE","CAROLYN","CHRISTINE","MARIE","JANET","CATHERINE","FRANCES", "ANN","JOYCE","DIANE","ALICE","JULIE","HEATHER","TERESA","DORIS","GLORIA", "EVELYN","JEAN","CHERYL","MILDRED","KATHERINE","JOAN","ASHLEY","JUDITH", "ROSE","JANICE","KELLY","NICOLE","JUDY","CHRISTINA","KATHY","THERESA", "BEVERLY","DENISE","TAMMY","IRENE","JANE","LORI","RACHEL","MARILYN","ANDREA", "KATHRYN","LOUISE","SARA","ANNE","JACQUELINE","WANDA","BONNIE","JULIA","RUBY", "LOIS","TINA","PHYLLIS","NORMA","PAULA","DIANA","ANNIE","LILLIAN","EMILY", "ROBIN","PEGGY","CRYSTAL","GLADYS","RITA","DAWN","CONNIE","FLORENCE","TRACY", "EDNA","TIFFANY","CARMEN","ROSA","CINDY","GRACE","WENDY","VICTORIA","EDITH", "KIM","SHERRY","SYLVIA","JOSEPHINE","THELMA","SHANNON","SHEILA","ETHEL", "ELLEN","ELAINE","MARJORIE","CARRIE","CHARLOTTE","MONICA","ESTHER","PAULINE", "EMMA","JUANITA","ANITA","RHONDA","HAZEL","AMBER","EVA","DEBBIE","APRIL", "LESLIE","CLARA","LUCILLE","JAMIE","JOANNE","ELEANOR","VALERIE","DANIELLE", "MEGAN","ALICIA","SUZANNE","MICHELE","GAIL","BERTHA","DARLENE","VERONICA", "JILL","ERIN","GERALDINE","LAUREN","CATHY","JOANN","LORRAINE","LYNN","SALLY", "REGINA","ERICA","BEATRICE","DOLORES","BERNICE","AUDREY","YVONNE","ANNETTE", "JUNE","SAMANTHA","MARION","DANA","STACY","ANA","RENEE","IDA","VIVIAN", "ROBERTA","HOLLY","BRITTANY","MELANIE","LORETTA","YOLANDA","JEANETTE", "LAURIE","KATIE","KRISTEN","VANESSA","ALMA","SUE","ELSIE","BETH","JEANNE", "VICKI","CARLA","TARA","ROSEMARY","EILEEN","TERRI","GERTRUDE","LUCY","TONYA", "ELLA","STACEY","WILMA","GINA","KRISTIN","JESSIE","NATALIE","AGNES","VERA", "WILLIE","CHARLENE","BESSIE","DELORES","MELINDA","PEARL","ARLENE","MAUREEN","COLLEEN", "ALLISON","TAMARA","JOY","GEORGIA","CONSTANCE","LILLIE","CLAUDIA", "JACKIE","MARCIA","TANYA","NELLIE", "MINNIE","MARLENE","HEIDI","GLENDA","LYDIA","VIOLA","COURTNEY","MARIAN","STELLA", "CAROLINE","DORA","JO","VICKIE","MATTIE","TERRY","MAXINE","IRMA","MABEL", "MARSHA","MYRTLE","LENA","CHRISTY", "DEANNA","PATSY","HILDA","GWENDOLYN","JENNIE","NORA","MARGIE","NINA","CASSANDRA", "LEAH","PENNY","KAY","PRISCILLA","NAOMI","CAROLE","BRANDY","OLGA", "BILLIE","DIANNE","TRACEY","LEONA","JENNY", "FELICIA","SONIA","MIRIAM","VELMA","BECKY","BOBBIE","VIOLET","KRISTINA","TONI","MISTY", "MAE","SHELLY","DAISY","RAMONA","SHERRI","ERIKA","KATRINA", "CLAIRE","LINDSEY","LINDSAY","GENEVA", "GUADALUPE","BELINDA","MARGARITA","SHERYL","CORA","FAYE","ADA","NATASHA","SABRINA", "ISABEL","MARGUERITE","HATTIE","HARRIET","MOLLY","CECILIA","KRISTI","BRANDI","BLANCHE", "SANDY","ROSIE","JOANNA","IRIS","EUNICE","ANGIE","INEZ","LYNDA", 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"CHARMAIN","CHARA","CAMMY","BEE","ARNETTE","ARDELLE","ANNIKA","AMIEE", "AMEE","ALLENA","YVONE","YUKI","YOSHIE","YEVETTE","YAEL","WILLETTA", "VONCILE","VENETTA","TULA","TONETTE","TIMIKA","TEMIKA","TELMA","TEISHA","TAREN","TA", "STACEE","SHIN","SHAWNTA","SATURNINA", "RICARDA","POK","PASTY","ONIE","NUBIA","MORA","MIKE","MARIELLE","MARIELLA","MARIANELA", "MARDELL","MANY","LUANNA","LOISE","LISABETH","LINDSY","LILLIANA", "LILLIAM","LELAH","LEIGHA","LEANORA","LANG", "KRISTEEN","KHALILAH","KEELEY","KANDRA","JUNKO","JOAQUINA", "JERLENE","JANI","JAMIKA","JAME","HSIU", "HERMILA","GOLDEN","GENEVIVE","EVIA","EUGENA","EMMALINE","ELFREDA","ELENE","DONETTE", "DELCIE","DEEANNA","DARCEY","CUC","CLARINDA","CIRA","CHAE","CELINDA","CATHERYN","CATHERIN", "CASIMIRA","CARMELIA","CAMELLIA","BREANA","BOBETTE","BERNARDINA","BEBE","BASILIA","ARLYNE", "AMAL","ALAYNA","ZONIA","ZENIA","YURIKO","YAEKO","WYNELL","WILLOW","WILLENA","VERNIA", "TU","TRAVIS","TORA","TERRILYN","TERICA","TENESHA","TAWNA","TAJUANA","TAINA", "STEPHNIE","SONA","SOL","SINA","SHONDRA", "SHIZUKO","SHERLENE","SHERICE","SHARIKA","ROSSIE","ROSENA","RORY","RIMA","RIA", "RHEBA","RENNA","PETER","NATALYA","NANCEE","MELODI","MEDA", "MAXIMA","MATHA","MARKETTA","MARICRUZ", "MARCELENE","MALVINA","LUBA","LOUETTA","LEIDA","LECIA","LAURAN","LASHAWNA","LAINE", "KHADIJAH","KATERINE","KASI","KALLIE","JULIETTA","JESUSITA","JESTINE", "JESSIA","JEREMY","JEFFIE","JANYCE","ISADORA","GEORGIANNE","FIDELIA","EVITA", "EURA","EULAH","ESTEFANA","ELSY","ELIZABET","ELADIA","DODIE","DION","DIA", "DENISSE","DELORAS","DELILA","DAYSI","DAKOTA","CURTIS","CRYSTLE","CONCHA","COLBY","CLARETTA", "CHU","CHRISTIA","CHARLSIE","CHARLENA","CARYLON","BETTYANN","ASLEY","ASHLEA", "AMIRA","AI","AGUEDA","AGNUS","YUETTE","VINITA", "VICTORINA","TYNISHA","TREENA","TOCCARA","TISH","THOMASENA","TEGAN","SOILA", "SHILOH","SHENNA","SHARMAINE","SHANTAE","SHANDI", "SEPTEMBER","SARAN","SARAI","SANA","SAMUEL", "SALLEY","ROSETTE","ROLANDE","REGINE","OTELIA","OSCAR","OLEVIA","NICHOLLE", "NECOLE","NAIDA","MYRTA","MYESHA","MITSUE","MINTA","MERTIE","MARGY","MAHALIA","MADALENE", "LOVE","LOURA","LOREAN","LEWIS","LESHA","LEONIDA","LENITA", "LAVONE","LASHELL","LASHANDRA","LAMONICA","KIMBRA","KATHERINA", "KARRY","KANESHA","JULIO","JONG","JENEVA", "JAQUELYN","HWA","GILMA","GHISLAINE","GERTRUDIS","FRANSISCA","FERMINA","ETTIE", "ETSUKO","ELLIS","ELLAN","ELIDIA","EDRA","DORETHEA", "DOREATHA","DENYSE","DENNY","DEETTA","DAINE","CYRSTAL", "CORRIN","CAYLA","CARLITA","CAMILA","BURMA","BULA","BUENA", "BLAKE","BARABARA","AVRIL","AUSTIN","ALAINE", "ZANA","WILHEMINA","WANETTA","VIRGIL","VI","VERONIKA", "VERNON","VERLINE","VASILIKI","TONITA","TISA","TEOFILA","TAYNA", "TAUNYA","TANDRA","TAKAKO","SUNNI","SUANNE", "SIXTA","SHARELL","SEEMA","RUSSELL","ROSENDA","ROBENA","RAYMONDE", "PEI","PAMILA","OZELL","NEIDA","NEELY","MISTIE","MICHA", "MERISSA","MAURITA","MARYLN","MARYETTA", "MARSHALL","MARCELL","MALENA","MAKEDA","MADDIE","LOVETTA","LOURIE", "LORRINE","LORILEE","LESTER","LAURENA","LASHAY","LARRAINE", "LAREE","LACRESHA","KRISTLE","KRISHNA", "KEVA","KEIRA","KAROLE","JOIE","JINNY","JEANNETTA","JAMA","HEIDY", "GILBERTE","GEMA","FAVIOLA","EVELYNN","ENDA","ELLI","ELLENA","DIVINA", "DAGNY","COLLENE","CODI","CINDIE", "CHASSIDY","CHASIDY","CATRICE","CATHERINA","CASSEY","CAROLL","CARLENA","CANDRA", "CALISTA","BRYANNA","BRITTENY","BEULA","BARI","AUDRIE","AUDRIA","ARDELIA", "ANNELLE","ANGILA","ALONA","ALLYN","DOUGLAS", "ROGER","JONATHAN","RALPH","NICHOLAS","BENJAMIN","BRUCE","HARRY","WAYNE", "STEVE","HOWARD","ERNEST","PHILLIP","TODD","CRAIG","ALAN","PHILIP","EARL","DANNY","BRYAN", "STANLEY","LEONARD","NATHAN","MANUEL","RODNEY","MARVIN","VINCENT","JEFFERY", "JEFF","CHAD","JACOB","ALFRED","BRADLEY","HERBERT","FREDERICK","EDWIN","DON","RICKY", "RANDALL","BARRY","BERNARD","LEROY","MARCUS","THEODORE","CLIFFORD","MIGUEL", "JIM","TOM","CALVIN","BILL","LLOYD","DEREK","WARREN","DARRELL","JEROME","FLOYD","ALVIN", "TIM","GORDON","GREG","JORGE","DUSTIN","PEDRO","DERRICK","ZACHARY","HERMAN", "GLEN","HECTOR","RICARDO","RICK","BRENT","RAMON","GILBERT","MARC","REGINALD", "RUBEN","NATHANIEL","RAFAEL","EDGAR","MILTON","RAUL","BEN", "CHESTER","DUANE","FRANKLIN","BRAD","RON","ROLAND","ARNOLD","HARVEY", "JARED","ERIK","DARRYL","NEIL","JAVIER","FERNANDO","CLINTON","TED","MATHEW","TYRONE", "DARREN","LANCE","KURT","ALLAN","NELSON","GUY","CLAYTON","HUGH", "MAX","DWAYNE","DWIGHT","ARMANDO","FELIX","EVERETT","IAN", "WALLACE","KEN","BOB","ALFREDO", "ALBERTO","DAVE","IVAN","BYRON","ISAAC","MORRIS","CLIFTON","WILLARD","ROSS", "ANDY","SALVADOR","KIRK","SERGIO","SETH","KENT","TERRANCE","EDUARDO", "TERRENCE","ENRIQUE","WADE","STUART","FREDRICK","ARTURO", "ALEJANDRO","NICK","LUTHER","WENDELL","JEREMIAH", "JULIUS","OTIS","TREVOR","OLIVER","LUKE","HOMER","GERARD","DOUG", "KENNY","HUBERT","LYLE","MATT","ALFONSO","ORLANDO","REX","CARLTON","ERNESTO", "NEAL","PABLO","LORENZO","OMAR","WILBUR","GRANT","HORACE", "RODERICK","ABRAHAM","WILLIS","RICKEY","ANDRES","CESAR","JOHNATHAN", "MALCOLM","RUDOLPH","DAMON","KELVIN", "PRESTON","ALTON","ARCHIE","MARCO","WM","PETE","RANDOLPH", "GARRY","GEOFFREY","JONATHON","FELIPE","GERARDO","ED","DOMINIC","DELBERT", "COLIN","GUILLERMO","EARNEST","LUCAS","BENNY","SPENCER", "RODOLFO","MYRON","EDMUND","GARRETT","SALVATORE", "CEDRIC","LOWELL","GREGG","SHERMAN","WILSON", "SYLVESTER","ROOSEVELT","ISRAEL","JERMAINE","FORREST", "WILBERT","LELAND","SIMON","CLARK","IRVING","BRYANT", "OWEN","RUFUS","WOODROW","KRISTOPHER","MACK", "LEVI","MARCOS","GUSTAVO","JAKE","LIONEL","GILBERTO","CLINT","NICOLAS", "ISMAEL","ORVILLE","ERVIN","DEWEY","AL","WILFRED","JOSH","HUGO","IGNACIO", "CALEB","TOMAS","SHELDON","ERICK","STEWART","DOYLE", "DARREL","ROGELIO","TERENCE","SANTIAGO","ALONZO","ELIAS", "BERT","ELBERT","RAMIRO","CONRAD","NOAH","GRADY","PHIL", "CORNELIUS","LAMAR","ROLANDO","CLAY", "PERCY","DEXTER","BRADFORD","DARIN","AMOS","MOSES", "IRVIN","SAUL","ROMAN","RANDAL","TIMMY","DARRIN","WINSTON", "BRENDAN","ABEL","DOMINICK","BOYD","EMILIO","ELIJAH","DOMINGO", "EMMETT","MARLON","EMANUEL","JERALD","EDMOND","EMIL","DEWAYNE","WILL","OTTO", "TEDDY","REYNALDO","BRET","JESS","TRENT","HUMBERTO","EMMANUEL", "STEPHAN","VICENTE","LAMONT","GARLAND","MILES", "EFRAIN","HEATH","RODGER","HARLEY","ETHAN","ELDON","ROCKY", "PIERRE","JUNIOR","FREDDY","ELI","BRYCE","ANTOINE", "STERLING","CHASE","GROVER","ELTON","CLEVELAND","DYLAN", "CHUCK","DAMIAN","REUBEN","STAN","AUGUST","LEONARDO","JASPER", "RUSSEL","ERWIN","BENITO","HANS","MONTE","BLAINE","ERNIE", "CURT","QUENTIN","AGUSTIN","MURRAY","JAMAL","ADOLFO", "HARRISON","TYSON","BURTON","BRADY","ELLIOTT","WILFREDO", "BART","JARROD","VANCE","DENIS","DAMIEN","JOAQUIN", "HARLAN","DESMOND","ELLIOT","DARWIN","GREGORIO", "BUDDY","XAVIER","KERMIT","ROSCOE","ESTEBAN","ANTON", "SOLOMON","SCOTTY","NORBERT","ELVIN","WILLIAMS","NOLAN", "ROD","QUINTON","HAL","BRAIN","ROB","ELWOOD","KENDRICK", "DARIUS","MOISES","FIDEL","THADDEUS","CLIFF","MARCEL","JACKSON", "RAPHAEL","BRYON","ARMAND","ALVARO", "JEFFRY","DANE","JOESPH","THURMAN","NED","RUSTY","MONTY", "FABIAN","REGGIE","MASON","GRAHAM","ISAIAH","VAUGHN","GUS","LOYD","DIEGO","ADOLPH", "NORRIS","MILLARD","ROCCO","GONZALO","DERICK","RODRIGO","WILEY", "RIGOBERTO","ALPHONSO","TY","NOE","VERN","REED", "JEFFERSON","ELVIS","BERNARDO","MAURICIO","HIRAM", "DONOVAN","BASIL","RILEY","NICKOLAS","MAYNARD","SCOT","VINCE", "QUINCY","EDDY","SEBASTIAN","FEDERICO", "ULYSSES","HERIBERTO","DONNELL","COLE","DAVIS","GAVIN","EMERY","WARD","ROMEO", "JAYSON","DANTE","CLEMENT","COY","MAXWELL","JARVIS","BRUNO", "ISSAC","DUDLEY","BROCK","SANFORD","CARMELO", "BARNEY","NESTOR","STEFAN","DONNY","ART","LINWOOD","BEAU", "WELDON","GALEN","ISIDRO","TRUMAN","DELMAR", "JOHNATHON","SILAS","FREDERIC","DICK","IRWIN","MERLIN", "CHARLEY","MARCELINO","HARRIS","CARLO","TRENTON","KURTIS","HUNTER","AURELIO","WINFRED", "VITO","COLLIN","DENVER","CARTER","LEONEL","EMORY","PASQUALE", "MOHAMMAD","MARIANO","DANIAL","LANDON", "DIRK","BRANDEN","ADAN","BUFORD","GERMAN","WILMER","EMERSON","ZACHERY", "FLETCHER","JACQUES","ERROL","DALTON","MONROE","JOSUE","EDWARDO","BOOKER","WILFORD", "SONNY","SHELTON","CARSON","THERON","RAYMUNDO","DAREN","HOUSTON", "ROBBY","LINCOLN","GENARO","BENNETT","OCTAVIO","CORNELL","HUNG","ARRON","ANTONY", "HERSCHEL","GIOVANNI","GARTH","CYRUS","CYRIL","RONNY","LON", "FREEMAN","DUNCAN","KENNITH","CARMINE","ERICH","CHADWICK","WILBURN","RUSS","REID","MYLES", "ANDERSON","MORTON","JONAS","FOREST","MITCHEL","MERVIN","ZANE","RICH", "JAMEL","LAZARO","ALPHONSE","RANDELL","MAJOR","JARRETT","BROOKS","ABDUL","LUCIANO", "SEYMOUR","EUGENIO","MOHAMMED","VALENTIN","CHANCE","ARNULFO","LUCIEN", "FERDINAND","THAD","EZRA","ALDO","RUBIN","ROYAL","MITCH","EARLE","ABE", "WYATT","MARQUIS","LANNY","KAREEM","JAMAR","BORIS","ISIAH","EMILE","ELMO","ARON", "LEOPOLDO","EVERETTE","JOSEF","ELOY","RODRICK","REINALDO", "LUCIO","JERROD","WESTON","HERSHEL", "BARTON","PARKER","LEMUEL","BURT","JULES","GIL","ELISEO","AHMAD","NIGEL", "EFREN","ANTWAN","ALDEN","MARGARITO","COLEMAN", "DINO","OSVALDO","LES","DEANDRE","NORMAND","KIETH","TREY","NORBERTO", "NAPOLEON","JEROLD","FRITZ","ROSENDO", "MILFORD","CHRISTOPER","ALFONZO","LYMAN","JOSIAH","BRANT","WILTON","RICO", "JAMAAL","DEWITT","BRENTON", "OLIN","FOSTER","FAUSTINO","CLAUDIO","JUDSON","GINO","EDGARDO","ALEC","TANNER", "JARRED","DONN","TAD","PRINCE","PORFIRIO","ODIS","LENARD","CHAUNCEY","TOD","MEL", "MARCELO","KORY","AUGUSTUS","KEVEN","HILARIO","BUD","SAL","ORVAL","MAURO","ZACHARIAH", "OLEN","ANIBAL","MILO","JED","DILLON","AMADO","NEWTON", "LENNY","RICHIE","HORACIO","BRICE","MOHAMED", "DELMER","DARIO","REYES","MAC","JONAH","JERROLD","ROBT","HANK","RUPERT","ROLLAND", "KENTON","DAMION","ANTONE","WALDO","FREDRIC","BRADLY","KIP","BURL","WALKER", "TYREE","JEFFEREY","AHMED","WILLY","STANFORD","OREN", "NOBLE","MOSHE","MIKEL","ENOCH","BRENDON", "QUINTIN","JAMISON","FLORENCIO","DARRICK","TOBIAS", "HASSAN","GIUSEPPE","DEMARCUS","CLETUS","TYRELL","LYNDON", "KEENAN","WERNER","GERALDO","COLUMBUS","CHET","BERTRAM", "MARKUS","HUEY","HILTON","DWAIN","DONTE","TYRON", "OMER","ISAIAS","HIPOLITO","FERMIN", "ADALBERTO","BO","BARRETT","TEODORO","MCKINLEY", "MAXIMO","GARFIELD","RALEIGH","LAWERENCE", "ABRAM","RASHAD","KING","EMMITT","DARON","SAMUAL","MIQUEL", "EUSEBIO","DOMENIC","DARRON","BUSTER","WILBER","RENATO","JC","HOYT","HAYWOOD", "EZEKIEL","CHAS","FLORENTINO","ELROY","CLEMENTE","ARDEN", "NEVILLE","EDISON","DESHAWN", "NATHANIAL","JORDON","DANILO","CLAUD","SHERWOOD","RAYMON", "RAYFORD","CRISTOBAL","AMBROSE","TITUS","HYMAN","FELTON", "EZEQUIEL","ERASMO","STANTON", "LONNY","LEN","IKE","MILAN","LINO","JAROD","HERB","ANDREAS", "WALTON","RHETT","PALMER","DOUGLASS","CORDELL","OSWALDO", "ELLSWORTH","VIRGILIO","TONEY", "NATHANAEL","DEL","BENEDICT","MOSE","JOHNSON","ISREAL","GARRET", "FAUSTO","ASA","ARLEN","ZACK","WARNER","MODESTO", "FRANCESCO","MANUAL","GAYLORD", "GASTON","FILIBERTO","DEANGELO","MICHALE","GRANVILLE","WES", "MALIK","ZACKARY","TUAN","ELDRIDGE","CRISTOPHER","CORTEZ","ANTIONE", "MALCOM","LONG","KOREY","JOSPEH","COLTON","WAYLON","VON","HOSEA","SHAD", "SANTO","RUDOLF","ROLF","REY","RENALDO","MARCELLUS","LUCIUS", "KRISTOFER","BOYCE","BENTON","HAYDEN","HARLAND", "ARNOLDO","RUEBEN","LEANDRO","KRAIG","JERRELL","JEROMY","HOBERT","CEDRICK", "ARLIE","WINFORD","WALLY","LUIGI","KENETH","JACINTO","GRAIG","FRANKLYN", "EDMUNDO","SID","PORTER","LEIF","JERAMY","BUCK","WILLIAN", "VINCENZO", "SHON","LYNWOOD","JERE","HAI","ELDEN","DORSEY","DARELL","BRODERICK","ALONSO"]; function opdracht22() { function letterwaarde(c) { return c > 64 ? c - 64 : c; } names22.sort(); var total = 0; for (var i = 0; i < 5163; i++) { var score = 0; for (var j = 0; j < names22[i].length; j++) score += letterwaarde(names22[i].charCodeAt(j)); score = score * (i + 1); total += score; } return total; } alert(opdracht22()); // should give 871,198,282

#23 Non-abundant sums

A perfect number is a number for which the sum of its proper divisors is exactly equal to the number. For example, the sum of the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number.

A number n is called deficient if the sum of its proper divisors is less than n and it is called abundant if this sum exceeds n.

As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the smallest number that can be written as the sum of two abundant numbers is 24. By mathematical analysis, it can be shown that all integers greater than 28123 can be written as the sum of two abundant numbers. However, this upper limit cannot be reduced any further by analysis even though it is known that the greatest number that cannot be expressed as the sum of two abundant numbers is less than this limit.

Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.

function opdracht23() { var xmax = 28123; var abundants = []; function divsum(n) { var xsum = 0; for (var i = 1; i <= Math.floor(n / 2); i++) if (n % i == 0) xsum += i; return xsum; } for (var i = 1; i <=xmax; i++) if (divsum(i) > i) abundants.push(i); var xsum = 1; function binarySearch(d, n) { var first = 0, last = d.length - 1; var middle = Math.floor((first + last) / 2); while (first <= last) { if (d[middle] < n) first = middle + 1; else if (d[middle] == n) return true; else last = middle - 1; middle = Math.floor((first + last)/2); } return false; } for (var i = 2; i <= xmax; i++) { var boo = true; for (var j = 0; j < abundants.length; j++) { if (abundants[j] < i) { if (binarySearch(abundants, i - abundants[j])) { boo = false; break; } } else break; } if (boo === true) xsum += i; } return xsum; } alert(opdracht23()); // should give 4,179,871

#24: Lexicographic permutations

A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are:

012 021 102 120 201 210

What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?

function opdracht24(a = [0,1,2,3,4,5,6,7,8,9], perm = 10**6 - 1) { function concat(lst) { var ret = 0; for (i = 0; i < lst.length; i++) ret += lst[9 - i] * 10**i; return ret; } var b = a, permx = perm, lst = []; function factorial(n) { var xsum = 1; while (n > 1) xsum *= n--; return xsum; } for (var j = 0; j < 10; j++) { var fact = factorial(b.length - 1); var i = Math.floor(permx / fact); permx = permx % fact; lst.push(b[i]); b.splice(i, 1); } return concat(lst); } alert(opdracht24()); // should give 2,783,915,460

#25: 1000-digit Fibonacci number

The Fibonacci sequence is defined by the recurrence relation:

Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.

Hence the first 12 terms will be:

F1 = 1
F2 = 1
F3 = 2
F4 = 3
F5 = 5
F6 = 8
F7 = 13
F8 = 21
F9 = 34
F10 = 55
F11 = 89
F12 = 144

The 12th term, F12, is the first term to contain three digits.

What is the index of the first term in the Fibonacci sequence to contain 1000 digits?

/* https://www.mathblog.dk/project-euler-25-fibonacci-sequence-1000-digits/ */ function opdracht25() { return Math.floor((Math.log(10) * 999 + Math.log(5) / 2)/Math.log(1.6180)); } alert(opdracht25()); // should give 4,782

#26: Reciprocal cycles

A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given: 

1/2 =  0.5
1/3 =  0.(3)
1/4 =  0.25
1/5 =  0.2
1/6 =  0.1(6)
1/7 =  0.(142857)
1/8 =  0.125
1/9 =  0.(1)
1/10 =  0.1

Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.

Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.

function opdracht26() { var sieve = Array(1000).fill(true); sieve[0] = sieve[1] = false; for (var i = 0; i < sieve.length; i++) if (sieve[i]) for (var j = i * i; j < sieve.length; j+= i) sieve[j] = false; var primes = []; for (var i = 0; i < sieve.length; i++) if (sieve[i]) primes.push(i); function cycleLength(n) { for (var a = 1, t = 0; true;) { a = a * 10 % n, t++; if (a == 0) return 0; if (a == 1) return t; } return 0; } var best = 0; for (var i = 0; i < primes.length; i++) if (cycleLength(primes[i]) == primes[i] - 1) best = primes[i]; return best; } alert(opdracht26()); // should give 983

#27: Quadratic primes

function opdracht27() { function isprime(n) { var presets = [300, 100, 8]; var top = n; for (var i = 0; i < presets.length; i++) if (n > presets[i] * presets[i]) top = Math.floor(n / presets[i]); for (var i = 2; i < top; i++) if (n % i == 0) return false; return true; } var best_a = 0, best_b = 0, best_n = 0; for (var a = -999; a < 1000; a++) { for (var b = -1000; b <= 1000; b++) { var n = 0; while (isprime(Math.abs(n * n + a * n + b))) n++; if (n > best_n) best_a = a, best_b = b, best_n = n; } } return best_a * best_b; } alert(opdracht27()); // should give -59231

#28 Number spiral diagonals

Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows: 

21 22 23 24 25
20  7  8  9 10
19  6  1  2 11
18  5  4  3 12
17 16 15 14 13

It can be verified that the sum of the numbers on the diagonals is 101. What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?

function opdracht28(root = 1001) { var xsum = 1, ring = 24, step = 52; for (var i = 0; i < Math.floor(root / 2); i++) xsum += ring, ring += step, step += 32; return xsum; } function opdracht28b(root = 1001) { var xsum = 1, foo = 1, step = 2; for (var step = 2; foo < root * root; step += 2) for (var i = 0; i < 4; i++) foo += step, xsum += foo; return xsum; } alert(opdracht28()); // should give 669,171,001

#29: Distinct powers

Consider all integer combinations of a^b for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5: 

2^2=4, 2^3=8, 2^4=16, 2^5=32
3^2=9, 3^3=27, 3^4=81, 3^5=243
4^2=16, 4^3=64, 4^4=256, 4^5=1024
5^2=25, 5^3=125, 5^4=625, 5^5=3125

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

function opdracht29() { function myRoot(n) { for (var a = 2; a <= 10; a++) for (var e = 1, b = 0; (b = a**e) <= 100; e++) if (b == (n & 0xffff0000) >> 16) return a << 16 | e; return n; } function eqpow(n) { var root = myRoot(n); return (root & 0xffff0000) | (n & 0xffff) * (root &0xffff); } st = new Set(); for (var a = 2; a <= 100; a++) for (var b = 2; b <= 100; b++) { st.add(eqpow(a << 16 | b)); } return st.size; } alert(opdracht29()); // should give 9,183

#30: Digit fifth powers

Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits: 

1634 = 1^4 + 6^4 + 3^4 + 4^4
8208 = 8^4 + 2^4 + 0^4 + 8^4
9474 = 9^4 + 4^4 + 7^4 + 4^4

As 1 = 14 is not a sum it is not included.

The sum of these numbers is 1634 + 8208 + 9474 = 19316.

Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.

function opdracht30(p = 5) { function test(n, p) { var xsum = 0, tmp = n; while (tmp > 0) xsum += (tmp % 10)**p, tmp = Math.floor(tmp / 10); return xsum == n; } var xsum = 0; for (var i = 2; i < 10**6; i++) xsum += test(i, p) ? i : 0; return xsum; } alert(opdracht30()); // should give 443,839

#31: Coin sums

In England the currency is made up of pound, P, and pence, p, and there are eight coins in general circulation:

1p, 2p, 5p, 10p, 20p, 50p, P1 (100p) and P2 (200p).

It is possible to make £2 in the following way:

1×P1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p

How many different ways can £2 be made using any number of coins?

function opdracht31(target = 200, coins = [1,2,5,10,20,50,100,200]) { var ways = Array(target + 1).fill(0); ways[0] = 1; for (var i = 0; i < coins.length; i++) for (var j = coins[i]; j <= target; j++) ways[j] += ways[j - coins[i]]; return ways[target]; } alert(opdracht31()); // should give 73,682

#32: Pandigital products

We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital.

The product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital.

Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital. HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.

function opdracht32() { function linearSearch(a, n) { for (var i = 0; i < a.length; i++) if (a[i] === n) return i + 1; // leave 0 for not found return 0; } function hasDigitsOnce(n, nset) { for (var i = 0; i < n.length; i++) { var nseti = linearSearch(nset, n[i]); if (nseti) nset.splice(nseti - 1, 1); else return false; } return true; } function isPandigital(n) { var nset = []; for (var i = 1; i <= n.length; i++) nset.push(i); return hasDigitsOnce(n, nset); } function arrize(n) { var arr = []; for (; n; n = Math.floor(n / 10)) arr.push(n % 10); arr.reverse(); return arr; } var p = []; for (var i = 2; i < 60; i++) { var start = i < 10 ? 1234 : 123; for (var j = start; j < Math.floor(10**5/i); j++) { var tmp = []; if (isPandigital(tmp.concat(arrize(i), arrize(j), arrize(i*j)))) if (linearSearch(p, i * j) == 0) p.push(i*j); } } var sum = 0; for (var i = 0; i < p.length; i++) sum += p[i]; return sum; } alert(opdracht32()); // should give 45,228

#33: Digit cancelling fractions

The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that 49/98 = 4/8, which is correct, is obtained by cancelling the 9s.

We shall consider fractions like, 30/50 = 3/5, to be trivial examples.

There are exactly four non-trivial examples of this type of fraction, less than one in value, and containing two digits in the numerator and denominator.

If the product of these four fractions is given in its lowest common terms, find the value of the denominator.

function opdracht33() { var d = 1; for (var i = 1; i < 10; i++) { for (var j = 1; j < i; j++) { var a = 9*j*i, b = 10*j-i, q = Math.floor(a / b), r = a % b; if (r == 0 && q <= 9) d *= i/j; } } return Math.floor(d); } alert(opdracht33()); // should give 100

#34: Digit factorials

145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.

Find the sum of all numbers which are equal to the sum of the factorial of their digits.

Note: as 1! = 1 and 2! = 2 are not sums they are not included.

function opdracht34() { var factorials = [1,1,2,6,24,120,720,5040,40320,362880]; function facsumdig(n) { var som = 0; while (n > 0) som += factorials[n % 10], n = Math.floor(n / 10); return som; } var totalSum = 0; for (var k = 10; k < factorials[9] * 7; k++) if (facsumdig(k) == k) totalSum += k; return totalSum; } alert(opdracht34()); // should give 40,730

#35: Circular primes

The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.

There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.

How many circular primes are there below one million?

function opdracht35(limit = 10**6-1) { function binarySearch(d, n) { var first = 0, last = d.length - 1; var middle = (first + last) >> 1; while (first <= last) { if (d[middle] < n) first = middle + 1; else if (d[middle] == n) return true; else last = middle - 1; middle = (first + last) >> 1; } return false; } function isCircular(n, lst) { function rotations(n) { function decimals(n) { var i = 0; while (n > 10**i) i++; return i; } function rotate(n) { var length = decimals(n), digit = n % 10,n = Math.floor(n / 10); n += digit * 10**(length - 1); return n; } var ret = []; for (var i = 0; i < decimals(n); i++) n = rotate(n), ret.push(n); return ret; } var rts = rotations(n); for (var i = 0; i < rts.length; i++) if (binarySearch(lst, rts[i]) == false) return false; return true; } var a = Array(limit).fill(true); a[0] = a[1] = false; for (var p = 2; p * p <= a.length; p++) if (a[p] == true) for (i = p * 2; i <= a.length; i += p) a[i] = false; var primes = []; for (var i = 0; i < a.length; i++) if (a[i]) primes.push(i); cprimes = []; for (var i = 0; i < primes.length; i++) if (isCircular(primes[i], primes)) cprimes.push(primes[i]); return cprimes.length; } alert(opdracht35()); // should give 55

#36: Double-base palindromes

The decimal number, 585 = 1001001001_2 (binary), is palindromic in both bases.

Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.

(Please note that the palindromic number, in either base, may not include leading zeros.)

function opdracht36(limit = 10**6) { function ispalindrome(n, base = 10) { var rev = 0; for (var temp = n; temp != 0; temp = Math.floor(temp/base)) rev = rev * base + temp % base; return n == rev; } var xsum = 0; for (var i = 1; i < limit; i++) if (ispalindrome(i, 10) && ispalindrome(i, 2)) xsum += i; return xsum; } alert(opdracht36()); // should give 872,187

#37: Truncatable primes

The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.

Find the sum of the only eleven primes that are both truncatable from left to right and right to left.

NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.

function opdracht37() { function binarySearch(d, n) { var first = 0, last = d.length - 1; var middle = (first + last) >> 1; while (first <= last) { if (d[middle] < n) first = middle + 1; else if (d[middle] == n) return true; else last = middle - 1; middle = (first + last) >> 1; } return false; } function isrighttruncatable(primes, n) { while (n > 10) { n = Math.floor(n / 10); if (binarySearch(primes, n) == false) return false; } return true; } function islefttruncatable(primes, n) { function decimals(n) { var i = 0; while (n > 10**i) i++; return i; } function truncateLeft(n) { var exp = decimals(n) - 1; return n % 10**exp; } var length = decimals(n); for (var i = 0; i < length; i++) { if (binarySearch(primes, n) == false) return false; n = truncateLeft(n); } return true; } var a = Array(10**6).fill(true); a[0] = a[1] = false; for (var p = 2; p * p <= a.length; p++) if (a[p] == true) for (i = p * 2; i <= a.length; i += p) a[i] = false; var primes = []; for (var i = 0; i < a.length; i++) if (a[i]) primes.push(i); var xsum = 0; for (var i = 0; i < primes.length; i++) { if (primes[i] < 10) continue; if (isrighttruncatable(primes, primes[i]) && islefttruncatable(primes, primes[i])) xsum += primes[i]; } return xsum; } alert(opdracht37()); // should give 748,317

#38: Pandigital multiples

function opdracht38() { function decimals(n) { var i = 0; while (n >= 10**i) i++; return i; } function concat(a, b) { return b + a * 10**decimals(b); } function linearSearch(d, n) { for (var i = 0; i < d.length; i++) if (d[i] == n) return i + 1; return 0; } function hasDigitsOnce(n, nset) { while (n) { var i = linearSearch(nset, n % 10); if (i) nset.splice(i - 1, 1); else return false; n = Math.floor(n / 10); } return true; } function isPandigital(n) { var nset = []; for (var i = 1; i <= decimals(n); i++) nset.push(i); return hasDigitsOnce(n, nset); } for (var i = 9387; i > 9234; --i) { var result = concat(i, 2 * i); if (isPandigital(result)) return result; } return 0; } alert(opdracht38()); // should give 932,718,654

#39: Integer right triangles

If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.

{20,48,52}, {24,45,51}, {30,40,50}

For which value of p ≤ 1000, is the number of solutions maximised?

function opdracht39() { var best_p = 0, best_solutions = 0; for (var p = 100; p <= 1000; p += 2) { var solutions = 0; for (var a = 2; a < Math.floor(p / 3); a++) solutions += (p * (p - 2 * a) % (2 * (p - a)) == 0) ? 1 : 0; if (solutions > best_solutions) best_solutions = solutions, best_p = p; } return best_p; } alert(opdracht39()); // should give 840

#40: Champernowne's constant

An irrational decimal fraction is created by concatenating the positive integers:

0.123456789101112131415161718192021...

It can be seen that the 12th digit of the fractional part is 1.

If dn represents the nth digit of the fractional part, find the value of the following expression.

d1 × d10 × d100 × d1000 × d10000 × d100000 × d1000000

function opdracht40(indices = [0,9,99,999,9999,99999,999999]) { function getDigit(i) { function getDig(n, i) { var xdigits = []; while (n > 0) xdigits.push(n % 10), n = Math.floor(n / 10); var end = xdigits.length - 1; return xdigits[end - i]; } var offset = 0, decimals = 1, setLow = 1, setLength = 9; for (var limit = 9; i >= limit; limit += setLength * decimals) offset = limit, decimals++, setLow *= 10, setLength *= 10; n = Math.floor((i - offset) / decimals), ind = (i - offset) % decimals; return getDig(n + setLow, ind); } product = 1; for (var i = 0; i < indices.length; i++) product *= getDigit(indices[i]); return product; } alert(opdracht40()); // should give 210

#41: Pandigital prime

We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.

What is the largest n-digit pandigital prime that exists?

function opdracht41() { var sieve = Array(7654321).fill(true); sieve[0] = sieve[1] = false; for (var i = 0; i < sieve.length; i++) if (sieve[i]) for (var j = i * i; j < sieve.length; j+= i) sieve[j] = false; var primes = []; for (var i = 0; i < sieve.length; i++) if (sieve[i]) primes.push(i); var best = 0; function linearSearch(a, n) { for (var i = 0; i < a.length; i++) if (a[i] === n) return i + 1; // leave 0 for not found return 0; } function hasDigitsOnce(n, nset) { while (n > 0) { var nseti = linearSearch(nset, n % 10); if (nseti) nset.splice(nseti - 1, 1); else return false; n = Math.floor(n / 10); } return true; } function decimals(n) { var i = 0; while (n >= 10**i) i++; return i; } function isPandigital(n) { var nset = [], d = decimals(n); for (var i = 1; i <= d; i++) nset.push(i); return hasDigitsOnce(n, nset); } for (var i = 0; i < primes.length; i++) if (isPandigital(primes[i])) best = Math.max(best, primes[i]); return best; } alert(opdracht41()); // should give 7,652,413

#42: Coded triangle numbers

The nth term of the sequence of triangle numbers is given by, tn = 1/2n(n+1); so the first ten triangle numbers are:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for SKY is 19 + 11 + 25 = 55 = t10. If the word value is a triangle number then we shall call the word a triangle word.

Using words.txt (right click and 'Save Link/Target As...'), a 16K text file containing nearly two-thousand common English words, how many are triangle words?

var words42 = ["A","ABILITY","ABLE","ABOUT","ABOVE","ABSENCE","ABSOLUTELY","ACADEMIC", "ACCEPT","ACCESS","ACCIDENT","ACCOMPANY","ACCORDING","ACCOUNT", "ACHIEVE","ACHIEVEMENT","ACID","ACQUIRE","ACROSS","ACT","ACTION", "ACTIVE","ACTIVITY","ACTUAL","ACTUALLY","ADD","ADDITION","ADDITIONAL", "ADDRESS","ADMINISTRATION","ADMIT","ADOPT","ADULT","ADVANCE", "ADVANTAGE","ADVICE","ADVISE","AFFAIR","AFFECT","AFFORD","AFRAID", "AFTER","AFTERNOON","AFTERWARDS","AGAIN","AGAINST","AGE","AGENCY", "AGENT","AGO","AGREE","AGREEMENT","AHEAD","AID","AIM","AIR","AIRCRAFT", "ALL","ALLOW","ALMOST","ALONE","ALONG","ALREADY","ALRIGHT","ALSO", "ALTERNATIVE","ALTHOUGH","ALWAYS","AMONG","AMONGST","AMOUNT","AN", "ANALYSIS","ANCIENT","AND","ANIMAL","ANNOUNCE","ANNUAL","ANOTHER", "ANSWER","ANY","ANYBODY","ANYONE","ANYTHING","ANYWAY","APART","APPARENT", "APPARENTLY","APPEAL","APPEAR","APPEARANCE","APPLICATION","APPLY", "APPOINT","APPOINTMENT","APPROACH","APPROPRIATE","APPROVE","AREA", "ARGUE","ARGUMENT","ARISE","ARM","ARMY","AROUND","ARRANGE","ARRANGEMENT", "ARRIVE","ART","ARTICLE","ARTIST","AS","ASK","ASPECT","ASSEMBLY","ASSESS", "ASSESSMENT","ASSET","ASSOCIATE","ASSOCIATION","ASSUME","ASSUMPTION","AT", "ATMOSPHERE","ATTACH","ATTACK","ATTEMPT","ATTEND","ATTENTION","ATTITUDE", "ATTRACT","ATTRACTIVE","AUDIENCE","AUTHOR","AUTHORITY","AVAILABLE", "AVERAGE","AVOID","AWARD","AWARE","AWAY","AYE","BABY","BACK","BACKGROUND", "BAD","BAG","BALANCE","BALL","BAND","BANK","BAR","BASE","BASIC","BASIS", "BATTLE","BE","BEAR","BEAT","BEAUTIFUL","BECAUSE","BECOME","BED","BEDROOM", "BEFORE","BEGIN","BEGINNING","BEHAVIOUR","BEHIND","BELIEF","BELIEVE", "BELONG","BELOW","BENEATH","BENEFIT","BESIDE","BEST","BETTER","BETWEEN", "BEYOND","BIG","BILL","BIND","BIRD","BIRTH","BIT","BLACK","BLOCK","BLOOD", "BLOODY","BLOW","BLUE","BOARD","BOAT","BODY","BONE","BOOK","BORDER", "BOTH","BOTTLE","BOTTOM","BOX","BOY","BRAIN","BRANCH","BREAK","BREATH", "BRIDGE","BRIEF","BRIGHT","BRING","BROAD","BROTHER","BUDGET","BUILD", "BUILDING","BURN","BUS","BUSINESS","BUSY","BUT","BUY","BY","CABINET", "CALL","CAMPAIGN","CAN","CANDIDATE","CAPABLE","CAPACITY","CAPITAL","CAR", "CARD","CARE","CAREER","CAREFUL","CAREFULLY","CARRY","CASE","CASH","CAT", "CATCH","CATEGORY","CAUSE","CELL","CENTRAL","CENTRE","CENTURY","CERTAIN", "CERTAINLY","CHAIN","CHAIR","CHAIRMAN","CHALLENGE","CHANCE","CHANGE", "CHANNEL","CHAPTER","CHARACTER","CHARACTERISTIC","CHARGE","CHEAP","CHECK", "CHEMICAL","CHIEF","CHILD","CHOICE","CHOOSE","CHURCH","CIRCLE", "CIRCUMSTANCE","CITIZEN","CITY","CIVIL","CLAIM","CLASS","CLEAN","CLEAR", "CLEARLY","CLIENT","CLIMB","CLOSE","CLOSELY","CLOTHES","CLUB","COAL", "CODE","COFFEE","COLD","COLLEAGUE","COLLECT","COLLECTION","COLLEGE", "COLOUR","COMBINATION","COMBINE","COME","COMMENT","COMMERCIAL", "COMMISSION","COMMIT","COMMITMENT","COMMITTEE","COMMON","COMMUNICATION", "COMMUNITY","COMPANY","COMPARE","COMPARISON","COMPETITION","COMPLETE", "COMPLETELY","COMPLEX","COMPONENT","COMPUTER","CONCENTRATE", "CONCENTRATION","CONCEPT","CONCERN","CONCERNED","CONCLUDE","CONCLUSION", "CONDITION","CONDUCT","CONFERENCE","CONFIDENCE","CONFIRM","CONFLICT", "CONGRESS","CONNECT","CONNECTION","CONSEQUENCE","CONSERVATIVE","CONSIDER", "CONSIDERABLE","CONSIDERATION","CONSIST","CONSTANT","CONSTRUCTION", "CONSUMER","CONTACT","CONTAIN","CONTENT","CONTEXT","CONTINUE","CONTRACT", "CONTRAST","CONTRIBUTE","CONTRIBUTION","CONTROL","CONVENTION", "CONVERSATION","COPY","CORNER","CORPORATE","CORRECT","COS","COST","COULD", "COUNCIL","COUNT","COUNTRY","COUNTY","COUPLE","COURSE","COURT","COVER", "CREATE","CREATION","CREDIT","CRIME","CRIMINAL","CRISIS","CRITERION", "CRITICAL","CRITICISM","CROSS","CROWD","CRY","CULTURAL","CULTURE","CUP", "CURRENT","CURRENTLY","CURRICULUM","CUSTOMER","CUT","DAMAGE","DANGER", "DANGEROUS","DARK","DATA","DATE","DAUGHTER","DAY","DEAD","DEAL","DEATH", "DEBATE","DEBT","DECADE","DECIDE","DECISION","DECLARE","DEEP","DEFENCE", "DEFENDANT","DEFINE","DEFINITION","DEGREE","DELIVER","DEMAND","DEMOCRATIC", "DEMONSTRATE","DENY","DEPARTMENT","DEPEND","DEPUTY","DERIVE","DESCRIBE", "DESCRIPTION","DESIGN","DESIRE","DESK","DESPITE","DESTROY","DETAIL", "DETAILED","DETERMINE","DEVELOP","DEVELOPMENT","DEVICE","DIE","DIFFERENCE", "DIFFERENT","DIFFICULT","DIFFICULTY","DINNER","DIRECT","DIRECTION", "DIRECTLY","DIRECTOR","DISAPPEAR","DISCIPLINE","DISCOVER","DISCUSS", "DISCUSSION","DISEASE","DISPLAY","DISTANCE","DISTINCTION","DISTRIBUTION", "DISTRICT","DIVIDE","DIVISION","DO","DOCTOR","DOCUMENT","DOG","DOMESTIC", "DOOR","DOUBLE","DOUBT","DOWN","DRAW","DRAWING","DREAM","DRESS","DRINK", "DRIVE","DRIVER","DROP","DRUG","DRY","DUE","DURING","DUTY","EACH","EAR", "EARLY","EARN","EARTH","EASILY","EAST","EASY","EAT","ECONOMIC","ECONOMY", "EDGE","EDITOR","EDUCATION","EDUCATIONAL","EFFECT","EFFECTIVE", "EFFECTIVELY","EFFORT","EGG","EITHER","ELDERLY","ELECTION","ELEMENT", "ELSE","ELSEWHERE","EMERGE","EMPHASIS","EMPLOY","EMPLOYEE","EMPLOYER", "EMPLOYMENT","EMPTY","ENABLE","ENCOURAGE","END","ENEMY","ENERGY","ENGINE", "ENGINEERING","ENJOY","ENOUGH","ENSURE","ENTER","ENTERPRISE","ENTIRE", "ENTIRELY","ENTITLE","ENTRY","ENVIRONMENT","ENVIRONMENTAL","EQUAL", "EQUALLY","EQUIPMENT","ERROR","ESCAPE","ESPECIALLY","ESSENTIAL", "ESTABLISH","ESTABLISHMENT","ESTATE","ESTIMATE","EVEN","EVENING","EVENT", "EVENTUALLY","EVER","EVERY","EVERYBODY","EVERYONE","EVERYTHING","EVIDENCE", "EXACTLY","EXAMINATION","EXAMINE","EXAMPLE","EXCELLENT","EXCEPT","EXCHANGE", "EXECUTIVE","EXERCISE","EXHIBITION","EXIST","EXISTENCE","EXISTING","EXPECT", "EXPECTATION","EXPENDITURE","EXPENSE","EXPENSIVE","EXPERIENCE","EXPERIMENT", "EXPERT","EXPLAIN","EXPLANATION","EXPLORE","EXPRESS","EXPRESSION","EXTEND", "EXTENT","EXTERNAL","EXTRA","EXTREMELY","EYE","FACE","FACILITY","FACT", "FACTOR","FACTORY","FAIL","FAILURE","FAIR","FAIRLY","FAITH","FALL", "FAMILIAR","FAMILY","FAMOUS","FAR","FARM","FARMER","FASHION","FAST", "FATHER","FAVOUR","FEAR","FEATURE","FEE","FEEL","FEELING","FEMALE","FEW", "FIELD","FIGHT","FIGURE","FILE","FILL","FILM","FINAL","FINALLY","FINANCE", "FINANCIAL","FIND","FINDING","FINE","FINGER","FINISH","FIRE","FIRM","FIRST", "FISH","FIT","FIX","FLAT","FLIGHT","FLOOR","FLOW","FLOWER","FLY","FOCUS", "FOLLOW","FOLLOWING","FOOD","FOOT","FOOTBALL","FOR","FORCE","FOREIGN", "FOREST","FORGET","FORM","FORMAL","FORMER","FORWARD","FOUNDATION","FREE", "FREEDOM","FREQUENTLY","FRESH","FRIEND","FROM","FRONT","FRUIT","FUEL", "FULL","FULLY","FUNCTION","FUND","FUNNY","FURTHER","FUTURE","GAIN","GAME", "GARDEN","GAS","GATE","GATHER","GENERAL","GENERALLY","GENERATE", "GENERATION","GENTLEMAN","GET","GIRL","GIVE","GLASS","GO","GOAL","GOD", "GOLD","GOOD","GOVERNMENT","GRANT","GREAT","GREEN","GREY","GROUND","GROUP", "GROW","GROWING","GROWTH","GUEST","GUIDE","GUN","HAIR","HALF","HALL","HAND", "HANDLE","HANG","HAPPEN","HAPPY","HARD","HARDLY","HATE","HAVE","HE","HEAD", "HEALTH","HEAR","HEART","HEAT","HEAVY","HELL","HELP","HENCE","HER","HERE", "HERSELF","HIDE","HIGH","HIGHLY","HILL","HIM","HIMSELF","HIS","HISTORICAL", "HISTORY","HIT","HOLD","HOLE","HOLIDAY","HOME","HOPE","HORSE","HOSPITAL", "HOT","HOTEL","HOUR","HOUSE","HOUSEHOLD","HOUSING","HOW","HOWEVER","HUGE", "HUMAN","HURT","HUSBAND","I","IDEA","IDENTIFY","IF","IGNORE","ILLUSTRATE", "IMAGE","IMAGINE","IMMEDIATE","IMMEDIATELY","IMPACT","IMPLICATION","IMPLY", "IMPORTANCE","IMPORTANT","IMPOSE","IMPOSSIBLE","IMPRESSION","IMPROVE", "IMPROVEMENT","IN","INCIDENT","INCLUDE","INCLUDING","INCOME","INCREASE", "INCREASED","INCREASINGLY","INDEED","INDEPENDENT","INDEX","INDICATE", "INDIVIDUAL","INDUSTRIAL","INDUSTRY","INFLUENCE","INFORM","INFORMATION", "INITIAL","INITIATIVE","INJURY","INSIDE","INSIST","INSTANCE","INSTEAD", "INSTITUTE","INSTITUTION","INSTRUCTION","INSTRUMENT","INSURANCE","INTEND", "INTENTION","INTEREST","INTERESTED","INTERESTING","INTERNAL", "INTERNATIONAL","INTERPRETATION","INTERVIEW","INTO","INTRODUCE", "INTRODUCTION","INVESTIGATE","INVESTIGATION","INVESTMENT","INVITE", "INVOLVE","IRON","IS","ISLAND","ISSUE","IT","ITEM","ITS","ITSELF","JOB", "JOIN","JOINT","JOURNEY","JUDGE","JUMP","JUST","JUSTICE","KEEP","KEY","KID", "KILL","KIND","KING","KITCHEN","KNEE","KNOW","KNOWLEDGE","LABOUR","LACK", "LADY","LAND","LANGUAGE","LARGE","LARGELY","LAST","LATE","LATER","LATTER", "LAUGH","LAUNCH","LAW","LAWYER","LAY","LEAD","LEADER","LEADERSHIP", "LEADING","LEAF","LEAGUE","LEAN","LEARN","LEAST","LEAVE","LEFT","LEG", "LEGAL","LEGISLATION","LENGTH","LESS","LET","LETTER","LEVEL","LIABILITY", "LIBERAL","LIBRARY","LIE","LIFE","LIFT","LIGHT","LIKE","LIKELY","LIMIT", "LIMITED","LINE","LINK","LIP","LIST","LISTEN","LITERATURE","LITTLE","LIVE", "LIVING","LOAN","LOCAL","LOCATION","LONG","LOOK","LORD","LOSE","LOSS","LOT", "LOVE","LOVELY","LOW","LUNCH","MACHINE","MAGAZINE","MAIN","MAINLY", "MAINTAIN","MAJOR","MAJORITY","MAKE","MALE","MAN","MANAGE","MANAGEMENT", "MANAGER","MANNER","MANY","MAP","MARK","MARKET","MARRIAGE","MARRIED", "MARRY","MASS","MASTER","MATCH","MATERIAL","MATTER","MAY","MAYBE","ME", "MEAL","MEAN","MEANING","MEANS","MEANWHILE","MEASURE","MECHANISM","MEDIA", "MEDICAL","MEET","MEETING","MEMBER","MEMBERSHIP","MEMORY","MENTAL", "MENTION","MERELY","MESSAGE","METAL","METHOD","MIDDLE","MIGHT","MILE", "MILITARY","MILK","MIND","MINE","MINISTER","MINISTRY","MINUTE","MISS", "MISTAKE","MODEL","MODERN","MODULE","MOMENT","MONEY","MONTH","MORE", "MORNING","MOST","MOTHER","MOTION","MOTOR","MOUNTAIN","MOUTH","MOVE", "MOVEMENT","MUCH","MURDER","MUSEUM","MUSIC","MUST","MY","MYSELF","NAME", "NARROW","NATION","NATIONAL","NATURAL","NATURE","NEAR","NEARLY", "NECESSARILY","NECESSARY","NECK","NEED","NEGOTIATION","NEIGHBOUR","NEITHER", "NETWORK","NEVER","NEVERTHELESS","NEW","NEWS","NEWSPAPER","NEXT","NICE", "NIGHT","NO","NOBODY","NOD","NOISE","NONE","NOR","NORMAL","NORMALLY", "NORTH","NORTHERN","NOSE","NOT","NOTE","NOTHING","NOTICE","NOTION","NOW", "NUCLEAR","NUMBER","NURSE","OBJECT","OBJECTIVE","OBSERVATION","OBSERVE", "OBTAIN","OBVIOUS","OBVIOUSLY","OCCASION","OCCUR","ODD","OF","OFF", "OFFENCE","OFFER","OFFICE","OFFICER","OFFICIAL","OFTEN","OIL","OKAY","OLD", "ON","ONCE","ONE","ONLY","ONTO","OPEN","OPERATE","OPERATION","OPINION", "OPPORTUNITY","OPPOSITION","OPTION","OR","ORDER","ORDINARY","ORGANISATION", "ORGANISE","ORGANIZATION","ORIGIN","ORIGINAL","OTHER","OTHERWISE","OUGHT", "OUR","OURSELVES","OUT","OUTCOME","OUTPUT","OUTSIDE","OVER","OVERALL","OWN", "OWNER","PACKAGE","PAGE","PAIN","PAINT","PAINTING","PAIR","PANEL","PAPER", "PARENT","PARK","PARLIAMENT","PART","PARTICULAR","PARTICULARLY","PARTLY", "PARTNER","PARTY","PASS","PASSAGE","PAST","PATH","PATIENT","PATTERN","PAY", "PAYMENT","PEACE","PENSION","PEOPLE","PER","PERCENT","PERFECT","PERFORM", "PERFORMANCE","PERHAPS","PERIOD","PERMANENT","PERSON","PERSONAL","PERSUADE", "PHASE","PHONE","PHOTOGRAPH","PHYSICAL","PICK","PICTURE","PIECE","PLACE", "PLAN","PLANNING","PLANT","PLASTIC","PLATE","PLAY","PLAYER","PLEASE", "PLEASURE","PLENTY","PLUS","POCKET","POINT","POLICE","POLICY","POLITICAL", "POLITICS","POOL","POOR","POPULAR","POPULATION","POSITION","POSITIVE", "POSSIBILITY","POSSIBLE","POSSIBLY","POST","POTENTIAL","POUND","POWER", "POWERFUL","PRACTICAL","PRACTICE","PREFER","PREPARE","PRESENCE","PRESENT", "PRESIDENT","PRESS","PRESSURE","PRETTY","PREVENT","PREVIOUS","PREVIOUSLY", "PRICE","PRIMARY","PRIME","PRINCIPLE","PRIORITY","PRISON","PRISONER", "PRIVATE","PROBABLY","PROBLEM","PROCEDURE","PROCESS","PRODUCE","PRODUCT", "PRODUCTION","PROFESSIONAL","PROFIT","PROGRAM","PROGRAMME","PROGRESS", "PROJECT","PROMISE","PROMOTE","PROPER","PROPERLY","PROPERTY","PROPORTION", "PROPOSE","PROPOSAL","PROSPECT","PROTECT","PROTECTION","PROVE","PROVIDE", "PROVIDED","PROVISION","PUB","PUBLIC","PUBLICATION","PUBLISH","PULL", "PUPIL","PURPOSE","PUSH","PUT","QUALITY","QUARTER","QUESTION","QUICK", "QUICKLY","QUIET","QUITE","RACE","RADIO","RAILWAY","RAIN","RAISE","RANGE", "RAPIDLY","RARE","RATE","RATHER","REACH","REACTION","READ","READER", "READING","READY","REAL","REALISE","REALITY","REALIZE","REALLY","REASON", "REASONABLE","RECALL","RECEIVE","RECENT","RECENTLY","RECOGNISE", "RECOGNITION","RECOGNIZE","RECOMMEND","RECORD","RECOVER","RED","REDUCE", "REDUCTION","REFER","REFERENCE","REFLECT","REFORM","REFUSE","REGARD", "REGION","REGIONAL","REGULAR","REGULATION","REJECT","RELATE","RELATION", "RELATIONSHIP","RELATIVE","RELATIVELY","RELEASE","RELEVANT","RELIEF", "RELIGION","RELIGIOUS","RELY","REMAIN","REMEMBER","REMIND","REMOVE", "REPEAT","REPLACE","REPLY","REPORT","REPRESENT","REPRESENTATION", "REPRESENTATIVE","REQUEST","REQUIRE","REQUIREMENT","RESEARCH","RESOURCE", "RESPECT","RESPOND","RESPONSE","RESPONSIBILITY","RESPONSIBLE","REST", "RESTAURANT","RESULT","RETAIN","RETURN","REVEAL","REVENUE","REVIEW", "REVOLUTION","RICH","RIDE","RIGHT","RING","RISE","RISK","RIVER","ROAD", "ROCK","ROLE","ROLL","ROOF","ROOM","ROUND","ROUTE","ROW","ROYAL","RULE", "RUN","RURAL","SAFE","SAFETY","SALE","SAME","SAMPLE","SATISFY","SAVE", "SAY","SCALE","SCENE","SCHEME","SCHOOL","SCIENCE","SCIENTIFIC","SCIENTIST", "SCORE","SCREEN","SEA","SEARCH","SEASON","SEAT","SECOND","SECONDARY", "SECRETARY","SECTION","SECTOR","SECURE","SECURITY","SEE","SEEK","SEEM", "SELECT","SELECTION","SELL","SEND","SENIOR","SENSE","SENTENCE","SEPARATE", "SEQUENCE","SERIES","SERIOUS","SERIOUSLY","SERVANT","SERVE","SERVICE", "SESSION","SET","SETTLE","SETTLEMENT","SEVERAL","SEVERE","SEX","SEXUAL", "SHAKE","SHALL","SHAPE","SHARE","SHE","SHEET","SHIP","SHOE","SHOOT","SHOP", "SHORT","SHOT","SHOULD","SHOULDER","SHOUT","SHOW","SHUT","SIDE","SIGHT", "SIGN","SIGNAL","SIGNIFICANCE","SIGNIFICANT","SILENCE","SIMILAR","SIMPLE", "SIMPLY","SINCE","SING","SINGLE","SIR","SISTER","SIT","SITE","SITUATION", "SIZE","SKILL","SKIN","SKY","SLEEP","SLIGHTLY","SLIP","SLOW","SLOWLY", "SMALL","SMILE","SO","SOCIAL","SOCIETY","SOFT","SOFTWARE","SOIL","SOLDIER", "SOLICITOR","SOLUTION","SOME","SOMEBODY","SOMEONE","SOMETHING","SOMETIMES", "SOMEWHAT","SOMEWHERE","SON","SONG","SOON","SORRY","SORT","SOUND","SOURCE", "SOUTH","SOUTHERN","SPACE","SPEAK","SPEAKER","SPECIAL","SPECIES","SPECIFIC", "SPEECH","SPEED","SPEND","SPIRIT","SPORT","SPOT","SPREAD","SPRING","STAFF", "STAGE","STAND","STANDARD","STAR","START","STATE","STATEMENT","STATION", "STATUS","STAY","STEAL","STEP","STICK","STILL","STOCK","STONE","STOP", "STORE","STORY","STRAIGHT","STRANGE","STRATEGY","STREET","STRENGTH", "STRIKE","STRONG","STRONGLY","STRUCTURE","STUDENT","STUDIO","STUDY","STUFF", "STYLE","SUBJECT","SUBSTANTIAL","SUCCEED","SUCCESS","SUCCESSFUL","SUCH", "SUDDENLY","SUFFER","SUFFICIENT","SUGGEST","SUGGESTION","SUITABLE","SUM", "SUMMER","SUN","SUPPLY","SUPPORT","SUPPOSE","SURE","SURELY","SURFACE", "SURPRISE","SURROUND","SURVEY","SURVIVE","SWITCH","SYSTEM","TABLE","TAKE", "TALK","TALL","TAPE","TARGET","TASK","TAX","TEA","TEACH","TEACHER", "TEACHING","TEAM","TEAR","TECHNICAL","TECHNIQUE","TECHNOLOGY","TELEPHONE", "TELEVISION","TELL","TEMPERATURE","TEND","TERM","TERMS","TERRIBLE","TEST", "TEXT","THAN","THANK","THANKS","THAT","THE","THEATRE","THEIR","THEM", "THEME","THEMSELVES","THEN","THEORY","THERE","THEREFORE","THESE","THEY", "THIN","THING","THINK","THIS","THOSE","THOUGH","THOUGHT","THREAT", "THREATEN","THROUGH","THROUGHOUT","THROW","THUS","TICKET","TIME","TINY", "TITLE","TO","TODAY","TOGETHER","TOMORROW","TONE","TONIGHT","TOO","TOOL", "TOOTH","TOP","TOTAL","TOTALLY","TOUCH","TOUR","TOWARDS","TOWN","TRACK", "TRADE","TRADITION","TRADITIONAL","TRAFFIC","TRAIN","TRAINING","TRANSFER", "TRANSPORT","TRAVEL","TREAT","TREATMENT","TREATY","TREE","TREND","TRIAL", "TRIP","TROOP","TROUBLE","TRUE","TRUST","TRUTH","TRY","TURN","TWICE","TYPE", "TYPICAL","UNABLE","UNDER","UNDERSTAND","UNDERSTANDING","UNDERTAKE", "UNEMPLOYMENT","UNFORTUNATELY","UNION","UNIT","UNITED","UNIVERSITY", "UNLESS","UNLIKELY","UNTIL","UP","UPON","UPPER","URBAN","US","USE","USED", "USEFUL","USER","USUAL","USUALLY","VALUE","VARIATION","VARIETY","VARIOUS", "VARY","VAST","VEHICLE","VERSION","VERY","VIA","VICTIM","VICTORY","VIDEO", "VIEW","VILLAGE","VIOLENCE","VISION","VISIT","VISITOR","VITAL","VOICE", "VOLUME","VOTE","WAGE","WAIT","WALK","WALL","WANT","WAR","WARM","WARN", "WASH","WATCH","WATER","WAVE","WAY","WE","WEAK","WEAPON","WEAR","WEATHER", "WEEK","WEEKEND","WEIGHT","WELCOME","WELFARE","WELL","WEST","WESTERN", "WHAT","WHATEVER","WHEN","WHERE","WHEREAS","WHETHER","WHICH","WHILE", "WHILST","WHITE","WHO","WHOLE","WHOM","WHOSE","WHY","WIDE","WIDELY","WIFE", "WILD","WILL","WIN","WIND","WINDOW","WINE","WING","WINNER","WINTER","WISH", "WITH","WITHDRAW","WITHIN","WITHOUT","WOMAN","WONDER","WONDERFUL","WOOD", "WORD","WORK","WORKER","WORKING","WORKS","WORLD","WORRY","WORTH","WOULD", "WRITE","WRITER","WRITING","WRONG","YARD","YEAH","YEAR","YES","YESTERDAY", "YET","YOU","YOUNG","YOUR","YOURSELF","YOUTH"]; function opdracht42(words = words42) { function triangler(n) { return n * (n + 1) >> 1; } var triangles = []; for (var i = 0; i < 20; i++) triangles[i] = triangler(i); function wordcount(word) { var count = 0; for (var i = 0; i < word.length; i++) count += word.charCodeAt(i) - 64; return count; } function linearSearch(a, n) { for (var i = 0; i < a.length; i++) if (a[i] === n) return i + 1; // leave 0 for not found return 0; } var ret = 0; for (var i = 0; i < words.length; i++) if (linearSearch(triangles, wordcount(words[i]))) ret++; return ret; } alert(opdracht42()); // should give 162

#43: Sub-string divisibility

The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.

Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this way, we note the following: 

d2d3d4=406 is divisible by 2
d3d4d5=063 is divisible by 3
d4d5d6=635 is divisible by 5
d5d6d7=357 is divisible by 7
d6d7d8=572 is divisible by 11
d7d8d9=728 is divisible by 13
d8d9d10=289 is divisible by 17

Find the sum of all 0 to 9 pandigital numbers with this property.

function opdracht43() { function permutations(pool) { ret = [], n = pool.length, c = Array(n).fill(0), i = 0, tmp = 0; ret.push(pool.slice()); while (i < n) { if (c[i] < i) { if (i % 2 == 0) tmp = pool[0], pool[0] = pool[i], pool[i] = tmp; else tmp = pool[c[i]], pool[c[i]] = pool[i], pool[i] = tmp; ret.push(pool.slice()); c[i]++, i = 0; } else c[i++] = 0; } return ret; } function concat(lst) { var ret = 0; for (var i = 0; i < lst.length; i++) ret += lst[i] * 10 ** i; return ret; } function test(n) { var divs = [17,13,11,7,5,3,2]; for (var i = 0; i < divs.length; i++) if ((Math.floor(n / 10**i) % 1000) % divs[i] != 0) return false; return true; } var ps = permutations([0,1,2,3,4,5,6,7,8,9]); var xsum = 0; for (var i = 0; i < ps.length; i++) if (test(concat(ps[i]))) xsum += concat(ps[i]); return xsum; } alert(opdracht43()); // should give 16,695,334,890

#44: Pentagon numbers

Pentagonal numbers are generated by the formula, Pn=n(3n−1)/2. The first ten pentagonal numbers are:

1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...

It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference, 70 − 22 = 48, is not pentagonal.

Find the pair of pentagonal numbers, Pj and Pk, for which their sum and difference are pentagonal and D = |Pk − Pj| is minimised; what is the value of D?

function opdracht44(window = 10**4) { function binSearch(d, n) { var first = 0, last = d.length - 1; var middle = (first + last) >> 1; while (first <= last) { if (d[middle] < n) first = middle + 1; else if (d[middle] == n) return true; else last = middle - 1; middle = (first + last) >> 1; } return false; } function pentagon(n) { return n * (3 * n - 1) / 2 |0; } var lpgs = []; for (var i = 1; i < window; i++) lpgs.push(pentagon(i)); for (var a = 0; a < lpgs.length; a++) for (var b = a; b < lpgs.length; b++) if (binSearch(lpgs, lpgs[a] + lpgs[b]) && binSearch(lpgs, lpgs[b] - lpgs[a])) return lpgs[b] - lpgs[a]; return 0; } alert(opdracht44()); // should give 5,482,660

#45: Triangular, pentagonal, and hexagonal

Triangle, pentagonal, and hexagonal numbers are generated by the following formulae: Triangle Tn=n(n+1)/2 1, 3, 6, 10, 15, ... Pentagonal Pn=n(3n−1)/2 1, 5, 12, 22, 35, ... Hexagonal Hn=n(2n−1) 1, 6, 15, 28, 45, ...

It can be verified that T285 = P165 = H143 = 40755.

Find the next triangle number that is also pentagonal and hexagonal.

function opdracht45() { function binSearch(d, n) { var first = 0, last = d.length - 1; var middle = (first + last) >> 1; while (first <= last) { if (d[middle] < n) first = middle + 1; else if (d[middle] == n) return true; else last = middle - 1; middle = (first + last) >> 1; } return false; } function triangle(n) { return Math.floor(n * (n + 1) / 2); } function pentagon(n) { return Math.floor(n * (3 * n - 1) / 2); } function hexagon(n) { return n * (2 * n - 1); } var ltriangle = [], lpentagon = [], lhexagon = []; for (var i = 286; i < 10**5; i++) ltriangle.push(triangle(i)); for (var i = 166; i < 10**5; i++) lpentagon.push(pentagon(i)); for (var i = 144; i < 10**5; i++) lhexagon.push(hexagon(i)); for (var i = 0; i < ltriangle.length; i++) if (binSearch(lpentagon, ltriangle[i]) && binSearch(lhexagon, ltriangle[i])) return ltriangle[i]; return 0; } alert(opdracht45()); // should give 1,533,776,805

#46: Goldbach's other conjecture

It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square. 

9 = 7 + 2×1^2
15 = 7 + 2×2^2
21 = 3 + 2×3^2
25 = 7 + 2×3^2
27 = 19 + 2×2^2
33 = 31 + 2×1^2

It turns out that the conjecture was false.

What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?

function opdracht46() { function binSearch(d, n) { var first = 0, last = d.length - 1; var middle = (first + last) >> 1; while (first <= last) { if (d[middle] < n) first = middle + 1; else if (d[middle] == n) return true; else last = middle - 1; middle = (first + last) >> 1; } return false; } var sieve = Array(10**6).fill(true); sieve[0] = sieve[1] = false; for (var i = 0; i < sieve.length; i++) if (sieve[i]) for (var j = i * i; j < sieve.length; j+= i) sieve[j] = false; var primes = [], squares = []; for (var i = 0; i < sieve.length; i++) if (sieve[i]) primes.push(i); for (var i = 0; i < 100; i++) squares.push(2*i**2); function pair(primes, squares, n) { for (var i = 0; i < primes.length; i++) { if (primes[i] > n) break; if (binSearch(squares, n - primes[i])) return true; } return false; } for (var i = 3; i < 9**9; i += 2) { if (binSearch(primes, i)) continue; if (pair(primes, squares, i) == false) return i; } return 0; } alert(opdracht46()); // should give 5,777

#47: Distinct primes factors

The first two consecutive numbers to have two distinct prime factors are: 14 = 2 × 7 15 = 3 × 5 The first three consecutive numbers to have three distinct prime factors are: 

644 = 2^2 × 7 × 23
645 = 3 × 5 × 43
646 = 2 × 17 × 19.

Find the first four consecutive integers to have four distinct prime factors each. What is the first of these numbers?

function opdracht47(distinct = 4) { function linearSearch(a, n) { for (var i = 0; i < a.length; i++) if (a[i] === n) return i + 1; // leave 0 for not found return 0; } var sieve = Array(10**6).fill(true); sieve[0] = sieve[1] = false; for (var i = 0; i < sieve.length; i++) if (sieve[i]) for (var j = i * i; j < sieve.length; j+= i) sieve[j] = false; var primes = []; for (var i = 0; i < sieve.length; i++) if (sieve[i]) primes.push(i); var chain = 0; function primefactor(primes, n) { for (var i = 0; true; i++) if (n % primes[i] == 0) return primes[i]; } function primefactors(primes, n) { var factors = []; while (true) { var factor = primefactor(primes, n); factors.push(factor); if (factor == n) break; n = n / factor |0; } return factors; } function distinctLen(l) { var tmp = []; for (var i = 0; i < l.length; i++) if (linearSearch(tmp, l[i]) == 0) tmp.push(l[i]); return tmp.length; } for (var i = 2; i < 9**9; i++) { if (distinctLen(primefactors(primes, i)) == distinct) chain++; else chain = 0; if (chain == distinct) return i - (distinct - 1); } return 0; } alert(opdracht47()); // should give 134,043

#48: Self powers

The series, 1^1 + 2^2 + 3^3 + ... + 10^10 = 10405071317.

Find the last ten digits of the series, 1^1 + 2^2 + 3^3 + ... + 1000^1000.

/* adapted from https://www.mathblog.dk/project-euler-48-last-ten-digits/ */ function opdracht48() { var result = 0, modulo = 10**10; for (var i = 1; i <= 1000; i++) { var temp = i; for (var j = 1; j < i; j++) temp *= i, temp %= modulo; result += temp, result %= modulo; } return result; } alert(opdracht48()); // should give 9,110,846,700

#49: Prime permutations

The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.

There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.

What 12-digit number do you form by concatenating the three terms in this sequence?

function opdracht49() { function linearSearch(d, n) { for (var i = 0; i < d.length; i++) if (d[i] == n) return i + 1; return 0; } function digits(n) { var ret = []; while (n > 0) ret.push(n % 10), n = Math.floor(n / 10); return ret; } function decimals(n) { var i = 0; while (n >= 10**i) i++; return i; } function factorial(n) { var xsum = 1; while (n > 1) xsum *= n--; return xsum; } function perms(n) { var a = digits(n); a.reverse(); var ret = []; for (var j = 0; j < factorial(decimals(n)); j++) { var perm = j; var b = a.slice(0); // clone array a var tmp = 0; while (b.length > 0) { var x = factorial(b.length - 1); var i = Math.floor(perm / x); perm = perm % x; tmp += b[i] * 10**(b.length - 1); b.splice(i, 1); } ret.push(tmp); } return ret; } function sequences() { var sv = Array(10**4).fill(true); sv[0] = sv[1] = false; for (var p = 2; p * p < sv.length; p++) if (sv[p] == true) for (var i = p * 2; i < sv.length; i += p) sv[i] = false; var sprimes4 = []; for (var i = 1000; i < sv.length; i++) if (sv[i]) sprimes4.push(i); var lseq = []; function hasAlready(d, p) { for (var i = 0; i < d.length; i++) for (var j = 0; j < d[i].length; j++) if (d[i][j] == p) return true; return false; } for (var j = 0; j < sprimes4.length; j++) { var tmp = []; var prime = sprimes4[j]; if (hasAlready(lseq, prime)) continue; var p = perms(prime); for (var i = 0; i < p.length; i++) if (linearSearch(sprimes4, p[i])) tmp.push(p[i]); lseq.push(tmp); } return lseq; } lseq = sequences(); function check(a) { if (linearSearch(a, 1487)) return 0; for (var i = 0; i < a.length; i++) if (linearSearch(a, a[i] + 3330) && linearSearch(a, a[i] + 6660)) return (a[i] + 6660) + (a[i] + 3330) * 10**4 + a[i] * 10**8; return 0; } for (var i = 0; i < lseq.length; i++) if (check(lseq[i])) return check(lseq[i]); return 0; } alert(opdracht49()); // should give 296,962,999,629

#50: Consecutive prime sum

The prime 41, can be written as the sum of six consecutive primes: 41 = 2 + 3 + 5 + 7 + 11 + 13

This is the longest sum of consecutive primes that adds to a prime below one-hundred.

The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953.

Which prime, below one-million, can be written as the sum of the most consecutive primes?

function opdracht50(max = 10**6-1) { var sieve = Array(max + 1).fill(true); sieve[0] = sieve[1] = false; for (var i = 0; i < sieve.length; i++) if (sieve[i]) for (var j = i * i; j < sieve.length; j+= i) sieve[j] = false; var primes = []; for (var i = 0; i < sieve.length; i++) if (sieve[i]) primes.push(i); var best_prime = 0, best_sum = 0 var xlen = primes.length; function linearSearch(lst, n) { for (var i = 0; i < lst.length; i++) if (lst[i] == n) return true; return false; } for (var i = 0; i < xlen; i++) { for (var j = i + best_sum; j < xlen; j++) { var xsum = 0; for (var k = i; k < j; k++) xsum += primes[k]; if (xsum > max) break; var sublen = (j + 1) - i; if (linearSearch(primes, xsum) && sublen > best_sum) best_sum = sublen, best_prime = xsum; } } return best_prime; } alert(opdracht50()); // should give 997651

#51: Prime digit replacements

By replacing the 1st digit of the 2-digit number *3, it turns out that six of the nine possible values: 13, 23, 43, 53, 73, and 83, are all prime.

By replacing the 3rd and 4th digits of 56**3 with the same digit, this 5-digit number is the first example having seven primes among the ten generated numbers, yielding the family: 56003, 56113, 56333, 56443, 56663, 56773, and 56993. Consequently 56003, being the first member of this family, is the smallest prime with this property.

Find the smallest prime which, by replacing part of the number (not necessarily adjacent digits) with the same digit, is part of an eight prime value family.

function opdracht51() { function binarize(n) { var div = 2, dec = 1, ret = []; while (n) { ret.push(n % div ? dec : 0); n -= n % div; div *= 2, dec *= 10; } return ret; } function binSearch(d, n) { var first = 0, last = d.length - 1; var middle = Math.floor((first + last) / 2); while (first <= last) { if (d[middle] < n) first = middle + 1; else if (d[middle] == n) return true; else last = middle - 1; middle = Math.floor((first + last)/2); } return false; } function digit(n, i) { return Math.floor(n / 10**i) % 10; } function decimals(n) { var i = 0; while (n >= 10**i) i++; return i; } var sieve = Array(8**7).fill(true); sieve[0] = sieve[1] = false; for (var i = 0; i < sieve.length; i++) if (sieve[i]) for (var j = i * i; j < sieve.length; j+= i) sieve[j] = false; var primes = []; for (var i = 0; i < sieve.length; i++) if (sieve[i]) primes.push(i); function primeFamily(primes, n, mask) { var xlen = decimals(n); var bins = binarize(mask); var ret = []; for (var i = 0; i < bins.length; i++) n -= bins[i] * digit(n, i); for (var i = 0; i <= 9; i++) { var tmp = n; for (var b = 0; b < bins.length; b++) tmp += bins[b] * i; if (decimals(tmp) == xlen && binSearch(primes, tmp)) ret.push(tmp); } return ret; } for (var i = 10; i < primes.length; i++) { for (var m = 1; m < 2**decimals(primes[i]); m++) { var pf = primeFamily(primes, primes[i], m); if (pf.length == 8) return Math.min.apply(Math, pf); } } return 0; } alert(opdracht51()); // should give 121,313

#52: Pandigital multiples

It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order.

Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits.

function opdracht52() { function linSearch(lst, n) { for (var i = 0; i < lst.length; i++) if (lst[i] == n) return i + 1; return 0; } function test(n) { function digits(n) { ret = []; while (n) ret.push(n % 10), n = Math.floor(n / 10); return ret; } function hasDigitsOnce(n, nset) { var digs = digits(n); for (var i = 0; i < digs.length; i++) { var nseti = linSearch(nset, digs[i]); if (nseti) nset.splice(nseti - 1, 1); else return false; } return true; } var nset = digits(n); for (var i = 2; i <= 6; i++) if (hasDigitsOnce(n * i, nset.slice()) == false) return false; return true; } for (var n = 2; true; n++) if (test(n)) return n; return 0; } alert(opdracht52()); // should give 142,857

#53: Combinatoric selections

There are exactly ten ways of selecting three from five, 12345: 123, 124, 125, 134, 135, 145, 234, 235, 245, and 345 In combinatorics, we use the notation, 5C3 = 10. In general, nCr = n! r!(n−r)! ,where r ≤ n, n! = n×(n−1)×...×3×2×1, and 0! = 1. It is not until n = 23, that a value exceeds one-million: 23C10 = 1144066. How many, not necessarily distinct, values of nCr, for 1 ≤ n ≤ 100, are greater than one-million?

function opdracht53() { function combinations(n, r) { function factorial(n) { var xsum = 1; for (var a = 2; a <= n; a++) xsum *= a; return xsum; } return Math.floor(factorial(n) / (factorial(r) * factorial(n - r))); } var xcount = 0; for (var n = 23; n <= 100; n++) { for (var r = 4; r < n - 3; r++) { if (combinations(n, r) >= 10**6) { xcount += n - r * 2 + 1; break; } } } return xcount; } alert(opdracht53()); // should give 4,075

#54 Poker hands

In the card game poker, a hand consists of five cards and are ranked, from lowest to highest, in the following way:

High Card
Highest value card. One Pair: Two cards of the same value. Two Pairs: Two different pairs. Three of a Kind: Three cards of the same value. Straight: All cards are consecutive values. Flush: All cards of the same suit. Full House: Three of a kind and a pair. Four of a Kind: Four cards of the same value.
Straight Flush
All cards are consecutive values of same suit.
Royal Flush
Ten, Jack, Queen, King, Ace, in same suit.

The cards are valued in the order: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace.

If two players have the same ranked hands then the rank made up of the highest value wins; for example, a pair of eights beats a pair of fives (see example 1 below). But if two ranks tie, for example, both players have a pair of queens, then highest cards in each hand are compared (see example 4 below); if the highest cards tie then the next highest cards are compared, and so on.

Consider the following five hands dealt to two players:

HandPlayer 1Player 2Winner
1 5H 5C 6S 7S KD
Pair of Fives		 2C 3S 8S 8D TD
Pair of Eights		 Player 2
2 5D 8C 9S JS AC
Highest card Ace		 2C 5C 7D 8S QH
Highest card Queen		 Player 1
3 2D 9C AS AH AC
Three Aces		 3D 6D 7D TD QD
Flush with Diamonds		 Player 2
4 4D 6S 9H QH QC
Pair of Queens
Highest card Nine		 3D 6D 7H QD QS
Pair of Queens
Highest card Seven		 Player 1
5 2H 2D 4C 4D 4S 3C 3D 3S 9S 9D Player 1 Full House Full House With Three Fours with Three Threes

The file, poker.txt, contains one-thousand random hands dealt to two players. Each line of the file contains ten cards (separated by a single space): the first five are Player 1's cards and the last five are Player 2's cards. You can assume that all hands are valid (no invalid characters or repeated cards), each player's hand is in no specific order, and in each hand there is a clear winner.

How many hands does Player 1 win?

hands54 = ["8C TS KC 9H 4S 7D 2S 5D 3S AC", "5C AD 5D AC 9C 7C 5H 8D TD KS", "3H 7H 6S KC JS QH TD JC 2D 8S", "TH 8H 5C QS TC 9H 4D JC KS JS", "7C 5H KC QH JD AS KH 4C AD 4S", "5H KS 9C 7D 9H 8D 3S 5D 5C AH", "6H 4H 5C 3H 2H 3S QH 5S 6S AS", "TD 8C 4H 7C TC KC 4C 3H 7S KS", "7C 9C 6D KD 3H 4C QS QC AC KH", "JC 6S 5H 2H 2D KD 9D 7C AS JS", "AD QH TH 9D 8H TS 6D 3S AS AC", "2H 4S 5C 5S TC KC JD 6C TS 3C", "QD AS 6H JS 2C 3D 9H KC 4H 8S", "KD 8S 9S 7C 2S 3S 6D 6S 4H KC", "3C 8C 2D 7D 4D 9S 4S QH 4H JD", "8C KC 7S TC 2D TS 8H QD AC 5C", "3D KH QD 6C 6S AD AS 8H 2H QS", "6S 8D 4C 8S 6C QH TC 6D 7D 9D", "2S 8D 8C 4C TS 9S 9D 9C AC 3D", "3C QS 2S 4H JH 3D 2D TD 8S 9H", "5H QS 8S 6D 3C 8C JD AS 7H 7D", "6H TD 9D AS JH 6C QC 9S KD JC", "AH 8S QS 4D TH AC TS 3C 3D 5C", "5S 4D JS 3D 8H 6C TS 3S AD 8C", "6D 7C 5D 5H 3S 5C JC 2H 5S 3D", "5H 6H 2S KS 3D 5D JD 7H JS 8H", "KH 4H AS JS QS QC TC 6D 7C KS", "3D QS TS 2H JS 4D AS 9S JC KD", "QD 5H 4D 5D KH 7H 3D JS KD 4H", "2C 9H 6H 5C 9D 6C JC 2D TH 9S", "7D 6D AS QD JH 4D JS 7C QS 5C", "3H KH QD AD 8C 8H 3S TH 9D 5S", "AH 9S 4D 9D 8S 4H JS 3C TC 8D", "2C KS 5H QD 3S TS 9H AH AD 8S", "5C 7H 5D KD 9H 4D 3D 2D KS AD", "KS KC 9S 6D 2C QH 9D 9H TS TC", "9C 6H 5D QH 4D AD 6D QC JS KH", "9S 3H 9D JD 5C 4D 9H AS TC QH", "2C 6D JC 9C 3C AD 9S KH 9D 7D", "KC 9C 7C JC JS KD 3H AS 3C 7D", "QD KH QS 2C 3S 8S 8H 9H 9C JC", "QH 8D 3C KC 4C 4H 6D AD 9H 9D", "3S KS QS 7H KH 7D 5H 5D JD AD", "2H 2C 6H TH TC 7D 8D 4H 8C AS", "4S 2H AC QC 3S 6D TH 4D 4C KH", "4D TC KS AS 7C 3C 6D 2D 9H 6C", "8C TD 5D QS 2C 7H 4C 9C 3H 9H", "5H JH TS 7S TD 6H AD QD 8H 8S", "5S AD 9C 8C 7C 8D 5H 9D 8S 2S", "4H KH KS 9S 2S KC 5S AD 4S 7D", "QS 9C QD 6H JS 5D AC 8D 2S AS", "KH AC JC 3S 9D 9S 3C 9C 5S JS", "AD 3C 3D KS 3S 5C 9C 8C TS 4S", "JH 8D 5D 6H KD QS QD 3D 6C KC", "8S JD 6C 3S 8C TC QC 3C QH JS", "KC JC 8H 2S 9H 9C JH 8S 8C 9S", "8S 2H QH 4D QC 9D KC AS TH 3C", "8S 6H TH 7C 2H 6S 3C 3H AS 7S", "QH 5S JS 4H 5H TS 8H AH AC JC", "9D 8H 2S 4S TC JC 3C 7H 3H 5C", "3D AD 3C 3S 4C QC AS 5D TH 8C", "6S 9D 4C JS KH AH TS JD 8H AD", "4C 6S 9D 7S AC 4D 3D 3S TC JD", "AD 7H 6H 4H JH KC TD TS 7D 6S", "8H JH TC 3S 8D 8C 9S 2C 5C 4D", "2C 9D KC QH TH QS JC 9C 4H TS", "QS 3C QD 8H KH 4H 8D TD 8S AC", "7C 3C TH 5S 8H 8C 9C JD TC KD", "QC TC JD TS 8C 3H 6H KD 7C TD", "JH QS KS 9C 6D 6S AS 9H KH 6H", "2H 4D AH 2D JH 6H TD 5D 4H JD", "KD 8C 9S JH QD JS 2C QS 5C 7C", "4S TC 7H 8D 2S 6H 7S 9C 7C KC", "8C 5D 7H 4S TD QC 8S JS 4H KS", "AD 8S JH 6D TD KD 7C 6C 2D 7D", "JC 6H 6S JS 4H QH 9H AH 4C 3C", "6H 5H AS 7C 7S 3D KH KC 5D 5C", "JC 3D TD AS 4D 6D 6S QH JD KS", "8C 7S 8S QH 2S JD 5C 7H AH QD", "8S 3C 6H 6C 2C 8D TD 7D 4C 4D", "5D QH KH 7C 2S 7H JS 6D QC QD", "AD 6C 6S 7D TH 6H 2H 8H KH 4H", "KS JS KD 5D 2D KH 7D 9C 8C 3D", "9C 6D QD 3C KS 3S 7S AH JD 2D", "AH QH AS JC 8S 8H 4C KC TH 7D", "JC 5H TD 7C 5D KD 4C AD 8H JS", "KC 2H AC AH 7D JH KH 5D 7S 6D", "9S 5S 9C 6H 8S TD JD 9H 6C AC", "7D 8S 6D TS KD 7H AC 5S 7C 5D", "AH QC JC 4C TC 8C 2H TS 2C 7D", "KD KC 6S 3D 7D 2S 8S 3H 5S 5C", "8S 5D 8H 4C 6H KC 3H 7C 5S KD", "JH 8C 3D 3C 6C KC TD 7H 7C 4C", "JC KC 6H TS QS TD KS 8H 8C 9S", "6C 5S 9C QH 7D AH KS KC 9S 2C", "4D 4S 8H TD 9C 3S 7D 9D AS TH", "6S 7D 3C 6H 5D KD 2C 5C 9D 9C", "2H KC 3D AD 3H QD QS 8D JC 4S", "8C 3H 9C 7C AD 5D JC 9D JS AS", "5D 9H 5C 7H 6S 6C QC JC QD 9S", "JC QS JH 2C 6S 9C QC 3D 4S TC", "4H 5S 8D 3D 4D 2S KC 2H JS 2C", "TD 3S TH KD 4D 7H JH JS KS AC", "7S 8C 9S 2D 8S 7D 5C AD 9D AS", "8C 7H 2S 6C TH 3H 4C 3S 8H AC", "KD 5H JC 8H JD 2D 4H TD JH 5C", "3D AS QH KS 7H JD 8S 5S 6D 5H", "9S 6S TC QS JC 5C 5D 9C TH 8C", "5H 3S JH 9H 2S 2C 6S 7S AS KS", "8C QD JC QS TC QC 4H AC KH 6C", "TC 5H 7D JH 4H 2H 8D JC KS 4D", "5S 9C KH KD 9H 5C TS 3D 7D 2D", "5H AS TC 4D 8C 2C TS 9D 3H 8D", "6H 8D 2D 9H JD 6C 4S 5H 5S 6D", "AD 9C JC 7D 6H 9S 6D JS 9H 3C", "AD JH TC QS 4C 5D 9S 7C 9C AH", "KD 6H 2H TH 8S QD KS 9D 9H AS", "4H 8H 8D 5H 6C AH 5S AS AD 8S", "QS 5D 4S 2H TD KS 5H AC 3H JC", "9C 7D QD KD AC 6D 5H QH 6H 5S", "KC AH QH 2H 7D QS 3H KS 7S JD", "6C 8S 3H 6D KS QD 5D 5C 8H TC", "9H 4D 4S 6S 9D KH QC 4H 6C JD", "TD 2D QH 4S 6H JH KD 3C QD 8C", "4S 6H 7C QD 9D AS AH 6S AD 3C", "2C KC TH 6H 8D AH 5C 6D 8S 5D", "TD TS 7C AD JC QD 9H 3C KC 7H", "5D 4D 5S 8H 4H 7D 3H JD KD 2D", "JH TD 6H QS 4S KD 5C 8S 7D 8H", "AC 3D AS 8C TD 7H KH 5D 6C JD", "9D KS 7C 6D QH TC JD KD AS KC", "JH 8S 5S 7S 7D AS 2D 3D AD 2H", "2H 5D AS 3C QD KC 6H 9H 9S 2C", "9D 5D TH 4C JH 3H 8D TC 8H 9H", "6H KD 2C TD 2H 6C 9D 2D JS 8C", "KD 7S 3C 7C AS QH TS AD 8C 2S", "QS 8H 6C JS 4C 9S QC AD TD TS", "2H 7C TS TC 8C 3C 9H 2D 6D JC", "TC 2H 8D JH KS 6D 3H TD TH 8H", "9D TD 9H QC 5D 6C 8H 8C KC TS", "2H 8C 3D AH 4D TH TC 7D 8H KC", "TS 5C 2D 8C 6S KH AH 5H 6H KC", "5S 5D AH TC 4C JD 8D 6H 8C 6C", "KC QD 3D 8H 2D JC 9H 4H AD 2S", "TD 6S 7D JS KD 4H QS 2S 3S 8C", "4C 9H JH TS 3S 4H QC 5S 9S 9C", "2C KD 9H JS 9S 3H JC TS 5D AC", "AS 2H 5D AD 5H JC 7S TD JS 4C", "2D 4S 8H 3D 7D 2C AD KD 9C TS", "7H QD JH 5H JS AC 3D TH 4C 8H", "6D KH KC QD 5C AD 7C 2D 4H AC", "3D 9D TC 8S QD 2C JC 4H JD AH", "6C TD 5S TC 8S AH 2C 5D AS AC", "TH 7S 3D AS 6C 4C 7H 7D 4H AH", "5C 2H KS 6H 7S 4H 5H 3D 3C 7H", "3C 9S AC 7S QH 2H 3D 6S 3S 3H", "2D 3H AS 2C 6H TC JS 6S 9C 6C", "QH KD QD 6D AC 6H KH 2C TS 8C", "8H 7D 3S 9H 5D 3H 4S QC 9S 5H", "2D 9D 7H 6H 3C 8S 5H 4D 3S 4S", "KD 9S 4S TC 7S QC 3S 8S 2H 7H", "TC 3D 8C 3H 6C 2H 6H KS KD 4D", "KC 3D 9S 3H JS 4S 8H 2D 6C 8S", "6H QS 6C TC QD 9H 7D 7C 5H 4D", "TD 9D 8D 6S 6C TC 5D TS JS 8H", "4H KC JD 9H TC 2C 6S 5H 8H AS", "JS 9C 5C 6S 9D JD 8H KC 4C 6D", "4D 8D 8S 6C 7C 6H 7H 8H 5C KC", "TC 3D JC 6D KS 9S 6H 7S 9C 2C", "6C 3S KD 5H TS 7D 9H 9S 6H KH", "3D QD 4C 6H TS AC 3S 5C 2H KD", "4C AS JS 9S 7C TS 7H 9H JC KS", "4H 8C JD 3H 6H AD 9S 4S 5S KS", "4C 2C 7D 3D AS 9C 2S QS KC 6C", "8S 5H 3D 2S AC 9D 6S 3S 4D TD", "QD TH 7S TS 3D AC 7H 6C 5D QC", "TC QD AD 9C QS 5C 8D KD 3D 3C", "9D 8H AS 3S 7C 8S JD 2D 8D KC", "4C TH AC QH JS 8D 7D 7S 9C KH", "9D 8D 4C JH 2C 2S QD KD TS 4H", "4D 6D 5D 2D JH 3S 8S 3H TC KH", "AD 4D 2C QS 8C KD JH JD AH 5C", "5C 6C 5H 2H JH 4H KS 7C TC 3H", "3C 4C QC 5D JH 9C QD KH 8D TC", "3H 9C JS 7H QH AS 7C 9H 5H JC", "2D 5S QD 4S 3C KC 6S 6C 5C 4C", "5D KH 2D TS 8S 9C AS 9S 7C 4C", "7C AH 8C 8D 5S KD QH QS JH 2C", "8C 9D AH 2H AC QC 5S 8H 7H 2C", "QD 9H 5S QS QC 9C 5H JC TH 4H", "6C 6S 3H 5H 3S 6H KS 8D AC 7S", "AC QH 7H 8C 4S KC 6C 3D 3S TC", "9D 3D JS TH AC 5H 3H 8S 3S TC", "QD KH JS KS 9S QC 8D AH 3C AC", "5H 6C KH 3S 9S JH 2D QD AS 8C", "6C 4D 7S 7H 5S JC 6S 9H 4H JH", "AH 5S 6H 9S AD 3S TH 2H 9D 8C", "4C 8D 9H 7C QC AD 4S 9C KC 5S", "9D 6H 4D TC 4C JH 2S 5D 3S AS", "2H 6C 7C KH 5C AD QS TH JD 8S", "3S 4S 7S AH AS KC JS 2S AD TH", "JS KC 2S 7D 8C 5C 9C TS 5H 9D", "7S 9S 4D TD JH JS KH 6H 5D 2C", "JD JS JC TH 2D 3D QD 8C AC 5H", "7S KH 5S 9D 5D TD 4S 6H 3C 2D", "4S 5D AC 8D 4D 7C AD AS AH 9C", "6S TH TS KS 2C QC AH AS 3C 4S", "2H 8C 3S JC 5C 7C 3H 3C KH JH", "7S 3H JC 5S 6H 4C 2S 4D KC 7H", "4D 7C 4H 9S 8S 6S AD TC 6C JC", "KH QS 3S TC 4C 8H 8S AC 3C TS", "QD QS TH 3C TS 7H 7D AH TD JC", "TD JD QC 4D 9S 7S TS AD 7D AC", "AH 7H 4S 6D 7C 2H 9D KS JC TD", "7C AH JD 4H 6D QS TS 2H 2C 5C", "TC KC 8C 9S 4C JS 3C JC 6S AH", "AS 7D QC 3D 5S JC JD 9D TD KH", "TH 3C 2S 6H AH AC 5H 5C 7S 8H", "QC 2D AC QD 2S 3S JD QS 6S 8H", "KC 4H 3C 9D JS 6H 3S 8S AS 8C", "7H KC 7D JD 2H JC QH 5S 3H QS", "9H TD 3S 8H 7S AC 5C 6C AH 7C", "8D 9H AH JD TD QS 7D 3S 9C 8S", "AH QH 3C JD KC 4S 5S 5D TD KS", "9H 7H 6S JH TH 4C 7C AD 5C 2D", "7C KD 5S TC 9D 6S 6C 5D 2S TH", "KC 9H 8D 5H 7H 4H QC 3D 7C AS", "6S 8S QC TD 4S 5C TH QS QD 2S", "8S 5H TH QC 9H 6S KC 7D 7C 5C", "7H KD AH 4D KH 5C 4S 2D KC QH", "6S 2C TD JC AS 4D 6C 8C 4H 5S", "JC TC JD 5S 6S 8D AS 9D AD 3S", "6D 6H 5D 5S TC 3D 7D QS 9D QD", "4S 6C 8S 3S 7S AD KS 2D 7D 7C", "KC QH JC AC QD 5D 8D QS 7H 7D", "JS AH 8S 5H 3D TD 3H 4S 6C JH", "4S QS 7D AS 9H JS KS 6D TC 5C", "2D 5C 6H TC 4D QH 3D 9H 8S 6C", "6D 7H TC TH 5S JD 5C 9C KS KD", "8D TD QH 6S 4S 6C 8S KC 5C TC", "5S 3D KS AC 4S 7D QD 4C TH 2S", "TS 8H 9S 6S 7S QH 3C AH 7H 8C", "4C 8C TS JS QC 3D 7D 5D 7S JH", "8S 7S 9D QC AC 7C 6D 2H JH KC", "JS KD 3C 6S 4S 7C AH QC KS 5H", "KS 6S 4H JD QS TC 8H KC 6H AS", "KH 7C TC 6S TD JC 5C 7D AH 3S", "3H 4C 4H TC TH 6S 7H 6D 9C QH", "7D 5H 4S 8C JS 4D 3D 8S QH KC", "3H 6S AD 7H 3S QC 8S 4S 7S JS", "3S JD KH TH 6H QS 9C 6C 2D QD", "4S QH 4D 5H KC 7D 6D 8D TH 5S", "TD AD 6S 7H KD KH 9H 5S KC JC", "3H QC AS TS 4S QD KS 9C 7S KC", "TS 6S QC 6C TH TC 9D 5C 5D KD", "JS 3S 4H KD 4C QD 6D 9S JC 9D", "8S JS 6D 4H JH 6H 6S 6C KS KH", "AC 7D 5D TC 9S KH 6S QD 6H AS", "AS 7H 6D QH 8D TH 2S KH 5C 5H", "4C 7C 3D QC TC 4S KH 8C 2D JS", "6H 5D 7S 5H 9C 9H JH 8S TH 7H", "AS JS 2S QD KH 8H 4S AC 8D 8S", "3H 4C TD KD 8C JC 5C QS 2D JD", "TS 7D 5D 6C 2C QS 2H 3C AH KS", "4S 7C 9C 7D JH 6C 5C 8H 9D QD", "2S TD 7S 6D 9C 9S QS KH QH 5C", "JC 6S 9C QH JH 8D 7S JS KH 2H", "8D 5H TH KC 4D 4S 3S 6S 3D QS", "2D JD 4C TD 7C 6D TH 7S JC AH", "QS 7S 4C TH 9D TS AD 4D 3H 6H", "2D 3H 7D JD 3D AS 2S 9C QC 8S", "4H 9H 9C 2C 7S JH KD 5C 5D 6H", "TC 9H 8H JC 3C 9S 8D KS AD KC", "TS 5H JD QS QH QC 8D 5D KH AH", "5D AS 8S 6S 4C AH QC QD TH 7H", "3H 4H 7D 6S 4S 9H AS 8H JS 9D", "JD 8C 2C 9D 7D 5H 5S 9S JC KD", "KD 9C 4S QD AH 7C AD 9D AC TD", "6S 4H 4S 9C 8D KS TC 9D JH 7C", "5S JC 5H 4S QH AC 2C JS 2S 9S", "8C 5H AS QD AD 5C 7D 8S QC TD", "JC 4C 8D 5C KH QS 4D 6H 2H 2C", "TH 4S 2D KC 3H QD AC 7H AD 9D", "KH QD AS 8H TH KC 8D 7S QH 8C", "JC 6C 7D 8C KH AD QS 2H 6S 2D", "JC KH 2D 7D JS QC 5H 4C 5D AD", "TS 3S AD 4S TD 2D TH 6S 9H JH", "9H 2D QS 2C 4S 3D KH AS AC 9D", "KH 6S 8H 4S KD 7D 9D TS QD QC", "JH 5H AH KS AS AD JC QC 5S KH", "5D 7D 6D KS KD 3D 7C 4D JD 3S", "AC JS 8D 5H 9C 3H 4H 4D TS 2C", "6H KS KH 9D 7C 2S 6S 8S 2H 3D", "6H AC JS 7S 3S TD 8H 3H 4H TH", "9H TC QC KC 5C KS 6H 4H AC 8S", "TC 7D QH 4S JC TS 6D 6C AC KH", "QH 7D 7C JH QS QD TH 3H 5D KS", "3D 5S 8D JS 4C 2C KS 7H 9C 4H", "5H 8S 4H TD 2C 3S QD QC 3H KC", "QC JS KD 9C AD 5S 9D 7D 7H TS", "8C JC KH 7C 7S 6C TS 2C QD TH", "5S 9D TH 3C 7S QH 8S 9C 2H 5H", "5D 9H 6H 2S JS KH 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QS KH JH 2C 5D AD", "3S 5H KC 6C 9H 3H 2H AD 7D 7S", "7S JS JH KD 8S 7D 2S 9H 7C 2H", "9H 2D 8D QC 6S AD AS 8H 5H 6C", "2S 7H 6C 6D 7D 8C 5D 9D JC 3C", "7C 9C 7H JD 2H KD 3S KH AD 4S", "QH AS 9H 4D JD KS KD TS KH 5H", "4C 8H 5S 3S 3D 7D TD AD 7S KC", "JS 8S 5S JC 8H TH 9C 4D 5D KC", "7C 5S 9C QD 2C QH JS 5H 8D KH", "TD 2S KS 3D AD KC 7S TC 3C 5D", "4C 2S AD QS 6C 9S QD TH QH 5C", "8C AD QS 2D 2S KC JD KS 6C JC", "8D 4D JS 2H 5D QD 7S 7D QH TS", "6S 7H 3S 8C 8S 9D QS 8H 6C 9S", "4S TC 2S 5C QD 4D QS 6D TH 6S", "3S 5C 9D 6H 8D 4C 7D TC 7C TD", "AH 6S AS 7H 5S KD 3H 5H AC 4C", "8D 8S AH KS QS 2C AD 6H 7D 5D", "6H 9H 9S 2H QS 8S 9C 5D 2D KD", "TS QC 5S JH 7D 7S TH 9S 9H AC", "7H 3H 6S KC 4D 6D 5C 4S QD TS", "TD 2S 7C QD 3H JH 9D 4H 7S 7H", "KS 3D 4H 5H TC 2S AS 2D 6D 7D", "8H 3C 7H TD 3H AD KC TH 9C KH", "TC 4C 2C 9S 9D 9C 5C 2H JD 3C", "3H AC TS 5D AD 8D 6H QC 6S 8C", "2S TS 3S JD 7H 8S QH 4C 5S 8D", "AC 4S 6C 3C KH 3D 7C 2D 8S 2H", "4H 6C 8S TH 2H 4S 8H 9S 3H 7S", "7C 4C 9C 2C 5C AS 5D 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JC KH JD 2H TD TC", "8H 6C 2H 2C KH 6H 9D QS QH 5H", "AC 7D 2S 3D QD JC 2D 8D JD JH", "2H JC 2D 7H 2C 3C 8D KD TD 4H", "3S 4H 6D 8D TS 3H TD 3D 6H TH", "JH JC 3S AC QH 9H 7H 8S QC 2C", "7H TD QS 4S 8S 9C 2S 5D 4D 2H", "3D TS 3H 2S QC 8H 6H KC JC KS", "5D JD 7D TC 8C 6C 9S 3D 8D AC", "8H 6H JH 6C 5D 8D 8S 4H AD 2C", "9D 4H 2D 2C 3S TS AS TC 3C 5D", "4D TH 5H KS QS 6C 4S 2H 3D AD", "5C KC 6H 2C 5S 3C 4D 2D 9H 9S", "JD 4C 3H TH QH 9H 5S AH 8S AC", "7D 9S 6S 2H TD 9C 4H 8H QS 4C", "3C 6H 5D 4H 8C 9C KC 6S QD QS", "3S 9H KD TC 2D JS 8C 6S 4H 4S", "2S 4C 8S QS 6H KH 3H TH 8C 5D", "2C KH 5S 3S 7S 7H 6C 9D QD 8D", "8H KS AC 2D KH TS 6C JS KC 7H", "9C KS 5C TD QC AH 6C 5H 9S 7C", "5D 4D 3H 4H 6S 7C 7S AH QD TD", "2H 7D QC 6S TC TS AH 7S 9D 3H", "TH 5H QD 9S KS 7S 7C 6H 8C TD", "TH 2D 4D QC 5C 7D JD AH 9C 4H", "4H 3H AH 8D 6H QC QH 9H 2H 2C", "2D AD 4C TS 6H 7S TH 4H QS TD", "3C KD 2H 3H QS JD TC QC 5D 8H", "KS JC QD TH 9S KD 8D 8C 2D 9C", "3C QD KD 6D 4D 8D AH AD QC 8S", "8H 3S 9D 2S 3H KS 6H 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"AC 2S 6S 7S JS QD 5C QS 6H AD", "5H TH QC 7H TC 3S 7C 6D KC 3D", "4H 3D QC 9S 8H 2C 3S JC KS 5C", "4S 6S 2C 6H 8S 3S 3D 9H 3H JS", "4S 8C 4D 2D 8H 9H 7D 9D AH TS", "9S 2C 9H 4C 8D AS 7D 3D 6D 5S", "6S 4C 7H 8C 3H 5H JC AH 9D 9C", "2S 7C 5S JD 8C 3S 3D 4D 7D 6S", "3C KC 4S 5D 7D 3D JD 7H 3H 4H", "9C 9H 4H 4D TH 6D QD 8S 9S 7S", "2H AC 8S 4S AD 8C 2C AH 7D TC", "TS 9H 3C AD KS TC 3D 8C 8H JD", "QC 8D 2C 3C 7D 7C JD 9H 9C 6C", "AH 6S JS JH 5D AS QC 2C JD TD", "9H KD 2H 5D 2D 3S 7D TC AH TS", "TD 8H AS 5D AH QC AC 6S TC 5H", "KS 4S 7H 4D 8D 9C TC 2H 6H 3H", "3H KD 4S QD QH 3D 8H 8C TD 7S", "8S JD TC AH JS QS 2D KH KS 4D", "3C AD JC KD JS KH 4S TH 9H 2C", "QC 5S JS 9S KS AS 7C QD 2S JD", "KC 5S QS 3S 2D AC 5D 9H 8H KS", "6H 9C TC AD 2C 6D 5S JD 6C 7C", "QS KH TD QD 2C 3H 8S 2S QC AH", "9D 9H JH TC QH 3C 2S JS 5C 7H", "6C 3S 3D 2S 4S QD 2D TH 5D 2C", "2D 6H 6D 2S JC QH AS 7H 4H KH", "5H 6S KS AD TC TS 7C AC 4S 4H", "AD 3C 4H QS 8C 9D KS 2H 2D 4D", "4S 9D 6C 6D 9C AC 8D 3H 7H KD", "JC AH 6C 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QC 5D 2H KC", "5S 8D KD 6H 4H QD QH 6D AH 3D", "7S KS 6C 2S 4D AC QS 5H TS JD", "7C 2D TC 5D QS AC JS QC 6C KC", "2C KS 4D 3H TS 8S AD 4H 7S 9S", "QD 9H QH 5H 4H 4D KH 3S JC AD", "4D AC KC 8D 6D 4C 2D KH 2C JD", "2C 9H 2D AH 3H 6D 9C 7D TC KS", "8C 3H KD 7C 5C 2S 4S 5H AS AH", "TH JD 4H KD 3H TC 5C 3S AC KH", "6D 7H AH 7S QC 6H 2D TD JD AS", "JH 5D 7H TC 9S 7D JC AS 5S KH", "2H 8C AD TH 6H QD KD 9H 6S 6C", "QH KC 9D 4D 3S JS JH 4H 2C 9H", "TC 7H KH 4H JC 7D 9S 3H QS 7S", "AD 7D JH 6C 7H 4H 3S 3H 4D QH", "JD 2H 5C AS 6C QC 4D 3C TC JH", "AC JD 3H 6H 4C JC AD 7D 7H 9H", "4H TC TS 2C 8C 6S KS 2H JD 9S", "4C 3H QS QC 9S 9H 6D KC 9D 9C", "5C AD 8C 2C QH TH QD JC 8D 8H", "QC 2C 2S QD 9C 4D 3S 8D JH QS", "9D 3S 2C 7S 7C JC TD 3C TC 9H", "3C TS 8H 5C 4C 2C 6S 8D 7C 4H", "KS 7H 2H TC 4H 2C 3S AS AH QS", "8C 2D 2H 2C 4S 4C 6S 7D 5S 3S", "TH QC 5D TD 3C QS KD KC KS AS", "4D AH KD 9H KS 5C 4C 6H JC 7S", "KC 4H 5C QS TC 2H JC 9S AH QH", "4S 9H 3H 5H 3C QD 2H QC JH 8H", "5D AS 7H 2C 3D JH 6H 4C 6S 7D", "9C JD 9H AH JS 8S QH 3H KS 8H", "3S AC QC TS 4D AD 3D AH 8S 9H", "7H 3H QS 9C 9S 5H JH JS AH AC", "8D 3C JD 2H AC 9C 7H 5S 4D 8H", "7C JH 9H 6C JS 9S 7H 8C 9D 4H", "2D AS 9S 6H 4D JS JH 9H AD QD", "6H 7S JH KH AH 7H TD 5S 6S 2C", "8H JH 6S 5H 5S 9D TC 4C QC 9S", "7D 2C KD 3H 5H AS QD 7H JS 4D", "TS QH 6C 8H TH 5H 3C 3H 9C 9D", "AD KH JS 5D 3H AS AC 9S 5C KC", "2C KH 8C JC QS 6D AH 2D KC TC", "9D 3H 2S 7C 4D 6D KH KS 8D 7D", "9H 2S TC JH AC QC 3H 5S 3S 8H", "3S AS KD 8H 4C 3H 7C JH QH TS", "7S 6D 7H 9D JH 4C 3D 3S 6C AS", "4S 2H 2C 4C 8S 5H KC 8C QC QD", "3H 3S 6C QS QC 2D 6S 5D 2C 9D", "2H 8D JH 2S 3H 2D 6C 5C 7S AD", "9H JS 5D QH 8S TS 2H 7S 6S AD", "6D QC 9S 7H 5H 5C 7D KC JD 4H", "QC 5S 9H 9C 4D 6S KS 2S 4C 7C", "9H 7C 4H 8D 3S 6H 5C 8H JS 7S", "2D 6H JS TD 4H 4D JC TH 5H KC", "AC 7C 8D TH 3H 9S 2D 4C KC 4D", "KD QS 9C 7S 3D KS AD TS 4C 4H", "QH 9C 8H 2S 7D KS 7H 5D KD 4C", "9C 2S 2H JC 6S 6C TC QC JH 5C", "7S AC 8H KC 8S 6H QS JC 3D 6S", "JS 2D JH 8C 4S 6H 8H 6D 5D AD", "6H 7D 2S 4H 9H 7C AS AC 8H 5S", "3C JS 4S 6D 5H 2S QH 6S 9C 2C", "3D 5S 6S 9S 4C QS 8D QD 8S TC", "9C 3D AH 9H 5S 2C 7D AD JC 3S", "7H TC AS 3C 6S 6D 7S KH KC 9H", "3S TC 8H 6S 5H JH 8C 7D AC 2S", "QD 9D 9C 3S JC 8C KS 8H 5D 4D", "JS AH JD 6D 9D 8C 9H 9S 8H 3H", "2D 6S 4C 4D 8S AD 4S TC AH 9H", "TS AC QC TH KC 6D 4H 7S 8C 2H", "3C QD JS 9D 5S JC AH 2H TS 9H", "3H 4D QH 5D 9C 5H 7D 4S JC 3S", "8S TH 3H 7C 2H JD JS TS AC 8D", "9C 2H TD KC JD 2S 8C 5S AD 2C", "3D KD 7C 5H 4D QH QD TC 6H 7D", "7H 2C KC 5S KD 6H AH QC 7S QH", "6H 5C AC 5H 2C 9C 2D 7C TD 2S", "4D 9D AH 3D 7C JD 4H 8C 4C KS", "TH 3C JS QH 8H 4C AS 3D QS QC", "4D 7S 5H JH 6D 7D 6H JS KH 3C", "QD 8S 7D 2H 2C 7C JC 2S 5H 8C", "QH 8S 9D TC 2H AD 7C 8D QD 6S", "3S 7C AD 9H 2H 9S JD TS 4C 2D", "3S AS 4H QC 2C 8H 8S 7S TD TC", "JH TH TD 3S 4D 4H 5S 5D QS 2C", "8C QD QH TC 6D 4S 9S 9D 4H QC", "8C JS 9D 6H JD 3H AD 6S TD QC", "KC 8S 3D 7C TD 7D 8D 9H 4S 3S", "6C 4S 3D 9D KD TC KC KS AC 5S", "7C 6S QH 3D JS KD 6H 6D 2D 8C", "JD 2S 5S 4H 8S AC 2D 6S TS 5C", "5H 8C 5S 3C 4S 3D 7C 8D AS 3H", "AS TS 7C 3H AD 7D JC QS 6C 6H", "3S 9S 4C AC QH 5H 5D 9H TS 4H", "6C 5C 7H 7S TD AD JD 5S 2H 2S", "7D 6C KC 3S JD 8D 8S TS QS KH", "8S QS 8D 6C TH AC AH 2C 8H 9S", "7H TD KH QH 8S 3D 4D AH JD AS", "TS 3D 2H JC 2S JH KH 6C QC JS", "KC TH 2D 6H 7S 2S TC 8C 9D QS", "3C 9D 6S KH 8H 6D 5D TH 2C 2H", "6H TC 7D AD 4D 8S TS 9H TD 7S", "JS 6D JD JC 2H AC 6C 3D KH 8D", "KH JD 9S 5D 4H 4C 3H 7S QS 5C", "4H JD 5D 3S 3C 4D KH QH QS 7S", "JD TS 8S QD AH 4C 6H 3S 5S 2C", "QS 3D JD AS 8D TH 7C 6S QC KS", "7S 2H 8C QC 7H AC 6D 2D TH KH", "5S 6C 7H KH 7D AH 8C 5C 7S 3D", "3C KD AD 7D 6C 4D KS 2D 8C 4S", "7C 8D 5S 2D 2S AH AD 2C 9D TD", "3C AD 4S KS JH 7C 5C 8C 9C TH", "AS TD 4D 7C JD 8C QH 3C 5H 9S", "3H 9C 8S 9S 6S QD KS AH 5H JH", "QC 9C 5S 4H 2H TD 7D AS 8C 9D", "8C 2C 9D KD TC 7S 3D KH QC 3C", "4D AS 4C QS 5S 9D 6S JD QH KS", "6D AH 6C 4C 5H TS 9H 7D 3D 5S", "QS JD 7C 8D 9C AC 3S 6S 6C KH", "8H JH 5D 9S 6D AS 6S 3S QC 7H", "QD AD 5C JH 2H AH 4H AS KC 2C", "JH 9C 2C 6H 2D JS 5D 9H KC 6D", "7D 9D KD TH 3H AS 6S QC 6H AD", "JD 4H 7D KC 3H JS 3C TH 3D QS", "4C 3H 8C QD 5H 6H AS 8H AD JD", "TH 8S KD 5D QC 7D JS 5S 5H TS", "7D KC 9D QS 3H 3C 6D TS 7S AH", "7C 4H 7H AH QC AC 4D 5D 6D TH", "3C 4H 2S KD 8H 5H JH TC 6C JD", "4S 8C 3D 4H JS TD 7S JH QS KD", "7C QC KD 4D 7H 6S AD TD TC KH", "5H 9H KC 3H 4D 3D AD 6S QD 6H", "TH 7C 6H TS QH 5S 2C KC TD 6S", "7C 4D 5S JD JH 7D AC KD KH 4H", "7D 6C 8D 8H 5C JH 8S QD TH JD", "8D 7D 6C 7C 9D KD AS 5C QH JH", "9S 2C 8C 3C 4C KS JH 2D 8D 4H", "7S 6C JH KH 8H 3H 9D 2D AH 6D", "4D TC 9C 8D 7H TD KS TH KD 3C", "JD 9H 8D QD AS KD 9D 2C 2S 9C", "8D 3H 5C 7H KS 5H QH 2D 8C 9H", "2D TH 6D QD 6C KC 3H 3S AD 4C", "4H 3H JS 9D 3C TC 5H QH QC JC", "3D 5C 6H 3S 3C JC 5S 7S 2S QH", "AC 5C 8C 4D 5D 4H 2S QD 3C 3H", "2C TD AH 9C KD JS 6S QD 4C QC", "QS 8C 3S 4H TC JS 3H 7C JC AD", "5H 4D 9C KS JC TD 9S TS 8S 9H", "QD TS 7D AS AC 2C TD 6H 8H AH", "6S AD 8C 4S 9H 8D 9D KH 8S 3C", "QS 4D 2D 7S KH JS JC AD 4C 3C", "QS 9S 7H KC TD TH 5H JS AC JH", "6D AC 2S QS 7C AS KS 6S KH 5S", "6D 8H KH 3C QS 2H 5C 9C 9D 6C", "JS 2C 4C 6H 7D JC AC QD TD 3H", "4H QC 8H JD 4C KD KS 5C KC 7S", "6D 2D 3H 2S QD 5S 7H AS TH 6S", "AS 6D 8D 2C 8S TD 8H QD JC AH", "9C 9H 2D TD QH 2H 5C TC 3D 8H", "KC 8S 3D KH 2S TS TC 6S 4D JH", "9H 9D QS AC KC 6H 5D 4D 8D AH", "9S 5C QS 4H 7C 7D 2H 8S AD JS", "3D AC 9S AS 2C 2D 2H 3H JC KH", "7H QH KH JD TC KS 5S 8H 4C 8D", "2H 7H 3S 2S 5H QS 3C AS 9H KD", "AD 3D JD 6H 5S 9C 6D AC 9S 3S", "3D 5D 9C 2D AC 4S 2S AD 6C 6S", "QC 4C 2D 3H 6S KC QH QD 2H JH", "QC 3C 8S 4D 9S 2H 5C 8H QS QD", "6D KD 6S 7H 3S KH 2H 5C JC 6C", "3S 9S TC 6S 8H 2D AD 7S 8S TS", "3C 6H 9C 3H 5C JC 8H QH TD QD", "3C JS QD 5D TD 2C KH 9H TH AS", "9S TC JD 3D 5C 5H AD QH 9H KC", "TC 7H 4H 8H 3H TD 6S AC 7C 2S", "QS 9D 5D 3C JC KS 4D 6C JH 2S", "9S 6S 3C 7H TS 4C KD 6D 3D 9C", "2D 9H AH AC 7H 2S JH 3S 7C QC", "QD 9H 3C 2H AC AS 8S KD 8C KH", "2D 7S TD TH 6D JD 8D 4D 2H 5S", "8S QH KD JD QS JH 4D KC 5H 3S", "3C KH QC 6D 8H 3S AH 7D TD 2D", "5S 9H QH 4S 6S 6C 6D TS TH 7S", "6C 4C 6D QS JS 9C TS 3H 8D 8S", "JS 5C 7S AS 2C AH 2H AD 5S TC", "KD 6C 9C 9D TS 2S JC 4H 2C QD", "QS 9H TC 3H KC KS 4H 3C AD TH", "KH 9C 2H KD 9D TC 7S KC JH 2D", "7C 3S KC AS 8C 5D 9C 9S QH 3H", "2D 8C TD 4C 2H QC 5D TC 2C 7D", "KS 4D 6C QH TD KH 5D 7C AD 8D", "2S 9S 8S 4C 8C 3D 6H QD 7C 7H", "6C 8S QH 5H TS 5C 3C 4S 2S 2H", "8S 6S 2H JC 3S 3H 9D 8C 2S 7H", "QC 2C 8H 9C AC JD 4C 4H 6S 3S", "3H 3S 7D 4C 9S 5H 8H JC 3D TC", "QH 2S 2D 9S KD QD 9H AD 6D 9C", "8D 2D KS 9S JC 4C JD KC 4S TH", "KH TS 6D 4D 5C KD 5H AS 9H AD", "QD JS 7C 6D 5D 5C TH 5H QH QS", "9D QH KH 5H JH 4C 4D TC TH 6C", "KH AS TS 9D KD 9C 7S 4D 8H 5S", "KH AS 2S 7D 9D 4C TS TH AH 7C", "KS 4D AC 8S 9S 8D TH QH 9D 5C", "5D 5C 8C QS TC 4C 3D 3S 2C 8D", "9D KS 2D 3C KC 4S 8C KH 6C JC", "8H AH 6H 7D 7S QD 3C 4C 6C KC", "3H 2C QH 8H AS 7D 4C 8C 4H KC", "QD 5S 4H 2C TD AH JH QH 4C 8S", "3H QS 5S JS 8H 2S 9H 9C 3S 2C", "6H TS 7S JC QD AC TD KC 5S 3H", "QH AS QS 7D JC KC 2C 4C 5C 5S", "QH 3D AS JS 4H 8D 7H JC 2S 9C", "5D 4D 2S 4S 9D 9C 2D QS 8H 7H", "6D 7H 3H JS TS AC 2D JH 7C 8S", "JH 5H KC 3C TC 5S 9H 4C 8H 9D", "8S KC 5H 9H AD KS 9D KH 8D AH", "JC 2H 9H KS 6S 3H QC 5H AH 9C", "5C KH 5S AD 6C JC 9H QC 9C TD", "5S 5D JC QH 2D KS 8H QS 2H TS", "JH 5H 5S AH 7H 3C 8S AS TD KH", "6H 3D JD 2C 4C KC 7S AH 6C JH", "4C KS 9D AD 7S KC 7D 8H 3S 9C", "7H 5C 5H 3C 8H QC 3D KH 6D JC", "2D 4H 5D 7D QC AD AH 9H QH 8H", "KD 8C JS 9D 3S 3C 2H 5D 6D 2S", "8S 6S TS 3C 6H 8D 5S 3H TD 6C", "KS 3D JH 9C 7C 9S QS 5S 4H 6H", "7S 6S TH 4S KC KD 3S JC JH KS", "7C 3C 2S 6D QH 2C 7S 5H 8H AH", "KC 8D QD 6D KH 5C 7H 9D 3D 9C", "6H 2D 8S JS 9S 2S 6D KC 7C TC", "KD 9C JH 7H KC 8S 2S 7S 3D 6H", "4H 9H 2D 4C 8H 7H 5S 8S 2H 8D", "AD 7C 3C 7S 5S 4D 9H 3D JC KH", "5D AS 7D 6D 9C JC 4C QH QS KH", "KD JD 7D 3D QS QC 8S 6D JS QD", "6S 8C 5S QH TH 9H AS AC 2C JD", "QC KS QH 7S 3C 4C 5C KC 5D AH", "6C 4H 9D AH 2C 3H KD 3D TS 5C", "TD 8S QS AS JS 3H KD AC 4H KS", "7D 5D TS 9H 4H 4C 9C 2H 8C QC", "2C 7D 9H 4D KS 4C QH AD KD JS", "QD AD AH KH 9D JS 9H JC KD JD", "8S 3C 4S TS 7S 4D 5C 2S 6H 7C", "JS 7S 5C KD 6D QH 8S TD 2H 6S", "QH 6C TC 6H TD 4C 9D 2H QC 8H", "3D TS 4D 2H 6H 6S 2C 7H 8S 6C", "9H 9D JD JH 3S AH 2C 6S 3H 8S", "2C QS 8C 5S 3H 2S 7D 3C AD 4S", "5C QC QH AS TS 4S 6S 4C 5H JS", "JH 5C TD 4C 6H JS KD KH QS 4H", "TC KH JC 4D 9H 9D 8D KC 3C 8H", "2H TC 8S AD 9S 4H TS 7H 2C 5C", "4H 2S 6C 5S KS AH 9C 7C 8H KD", "TS QH TD QS 3C JH AH 2C 8D 7D", "5D KC 3H 5S AC 4S 7H QS 4C 2H", "3D 7D QC KH JH 6D 6C TD TH KD", "5S 8D TH 6C 9D 7D KH 8C 9S 6D", "JD QS 7S QC 2S QH JC 4S KS 8D", "7S 5S 9S JD KD 9C JC AD 2D 7C", "4S 5H AH JH 9C 5D TD 7C 2D 6S", "KC 6C 7H 6S 9C QD 5S 4H KS TD", "6S 8D KS 2D TH TD 9H JD TS 3S", "KH JS 4H 5D 9D TC TD QC JD TS", "QS QD AC AD 4C 6S 2D AS 3H KC", "4C 7C 3C TD QS 9C KC AS 8D AD", "KC 7H QC 6D 8H 6S 5S AH 7S 8C", "3S AD 9H JC 6D JD AS KH 6S JH", "AD 3D TS KS 7H JH 2D JS QD AC", "9C JD 7C 6D TC 6H 6C JC 3D 3S", "QC KC 3S JC KD 2C 8D AH QS TS", "AS KD 3D JD 8H 7C 8C 5C QD 6C"]