Solutions to various problems from projecteuler.net.

• Go
  • 078 Coin partitions
• Julia
  • 026 Reciprocal cycles
  • 068 Magic 5-gon ring
  • 074 Digit factorial chains
  • 075 Singular integer right triangles
  • 078 Coin partitions
  • 078 Coin partitions (rec)
  • 087 Prime power triples
  • 092 Square digit chains
  • 096 Su Doku
  • 096 Su Doku (v2)
  • 125 Palindromic sums
  • 132 Large repunit factors
  • 132 Large repunit factors (v2)
  • 133 Repunit nonfactors
  • 133 Repunit nonfactors (v2)
  • 191 Prize Strings
  • 191 Prize Strings (v2)
  • 225 Tribonacci non-divisors
  • 288 An enormous factorial
  • 348 Sum of a square and a cube
  • 417 Reciprocal cycles II
  • 485 Maximum number of divisors
  • 512 Sums of totients of powers
  • 516 5-smooth totients
  • 565 Divisibility of sum of divisors
  • 581 47-smooth triangular numbers
  • 622 Riffle Shuffles
  • 675 2 to omega of n
  • 719 Number Splitting
  • 757 Stealthy Numbers
• PARI GP
  • 182 RSA encryption
  • 235 An Arithmetic Geometric sequence
  • 704 Factors of Two in Binomial Coefficients
• Perl
  • 011 Largest product in a grid
  • 014 Longest Collatz sequence
  • 018 Maximum path sum I
  • 023 Non-abundant sums
  • 023 Non-abundant sums (v2)
  • 027 Quadratic primes
  • 030 Digit fifth powers
  • 030 Digit fifth powers (v2)
  • 037 Truncatable primes
  • 039 Integer right triangles
  • 040 Champernowne's constant
  • 041 Pandigital prime
  • 043 Sub-string divisibility
  • 044 Pentagon numbers
  • 047 Distinct primes factors
  • 048 Self powers
  • 049 Prime permutations
  • 050 Consecutive prime sum
  • 050 Consecutive prime sum (v2)
  • 051 Prime digit replacements
  • 051 Prime digit replacements (v2)
  • 054 Poker hands
  • 057 Square root convergents
  • 058 Spiral primes
  • 060 Prime pair sets
  • 060 Prime pair sets (v2)
  • 061 Cyclical figurate numbers
  • 062 Cubic permutations
  • 062 Cubic permutations (v2)
  • 063 Powerful digit counts
  • 064 Odd period square roots
  • 066 Diophantine equation
  • 067 Maximum path sum II
  • 068 Magic 5-gon ring
  • 069 Totient maximum
  • 070 Totient permutation
  • 070 Totient permutation (v2)
  • 072 Counting fractions
  • 072 Counting fractions (v2)
  • 073 Counting fractions in a range
  • 073 Counting fractions in a range (comb)
  • 074 Digit factorial chains
  • 075 Singular integer right triangles
  • 076 Counting summations
  • 077 Prime summations
  • 077 Prime summations (unoptimized)
  • 078 Coin partitions
  • 078 Coin partitions (rec)
  • 079 Passcode derivation
  • 081 Path sum two ways
  • 082 Path sum three ways
  • 083 Path sum four ways
  • 085 Counting rectangles
  • 087 Prime power triples
  • 092 Square digit chains
  • 092 Square digit chains (v2)
  • 093 Arithmetic expressions
  • 094 Almost equilateral triangles
  • 095 Amicable chains
  • 096 Su Doku
  • 096 Su Doku (v2)
  • 098 Anagramic squares
  • 099 Largest exponential
  • 100 Arranged probability
  • 102 Triangle containment
  • 102 Triangle containment (v2)
  • 104 Pandigital Fibonacci ends
  • 108 Diophantine reciprocals I
  • 110 Diophantine reciprocals II
  • 110 Diophantine reciprocals II (oeis)
  • 111 Primes with runs (v2)
  • 112 Bouncy numbers
  • 118 Pandigital prime sets
  • 119 Digit power sum
  • 123 Prime square remainders
  • 124 Ordered radicals
  • 127 abc-hits
  • 129 Repunit divisibility
  • 130 Composites with prime repunit property
  • 130 Composites with prime repunit property (v2)
  • 131 Prime cube partnership
  • 132 Large repunit factors
  • 132 Large repunit factors (v2)
  • 133 Repunit nonfactors
  • 133 Repunit nonfactors (v2)
  • 134 Prime pair connection
  • 135 Same differences
  • 136 Singleton difference
  • 138 Special isosceles triangles
  • 142 Perfect Square Collection
  • 145 How many reversible numbers are there below one-billion
  • 146 Investigating a Prime Pattern
  • 160 Factorial trailing digits
  • 169 Exploring the number of different ways a number can be expressed as a sum of powers of 2
  • 173 Using up to one million tiles how many different hollow square laminae can be formed
  • 174 Counting the number of hollow square laminae that can form one two three distinct arrangements
  • 179 Consecutive positive divisors
  • 182 RSA encryption
  • 182 RSA encryption (v2)
  • 183 Maximum product of parts
  • 183 Maximum product of parts (v2)
  • 187 Semiprimes
  • 187 Semiprimes (v2)
  • 191 Prize Strings
  • 192 Best Approximations
  • 193 Squarefree Numbers
  • 193 Squarefree Numbers (v2)
  • 196 Prime triplets
  • 197 Investigating the behaviour of a recursively defined sequence
  • 203 Squarefree Binomial Coefficients
  • 204 Generalised Hamming Numbers
  • 204 Generalised Hamming Numbers (v2)
  • 206 Concealed Square
  • 207 Integer partition equations
  • 207 Integer partition equations (v2)
  • 211 Divisor Square Sum
  • 211 Divisor Square Sum (oeis)
  • 214 Totient Chains
  • 216 Investigating the primality of numbers of the form 2
  • 221 Alexandrian Integers
  • 225 Tribonacci non-divisors
  • 225 Tribonacci non-divisors (v2)
  • 231 The prime factorisation of binomial coefficients
  • 235 An Arithmetic Geometric sequence
  • 243 Resilience
  • 248 Numbers for which Euler's totient function equals 13
  • 271 Modular Cubes part 1
  • 273 Sum of Squares (v2)
  • 277 A Modified Collatz sequence
  • 288 An enormous factorial
  • 291 Panaitopol Primes
  • 293 Pseudo-Fortunate Numbers
  • 303 Multiples with small digits
  • 304 Primonacci
  • 320 Factorials divisible by a huge integer
  • 343 Fractional Sequences
  • 345 Matrix Sum
  • 345 Matrix Sum (v2)
  • 346 Strong Repunits
  • 347 Largest integer divisible by two primes
  • 348 Sum of a square and a cube
  • 349 Langton's ant
  • 357 Prime generating integers
  • 365 A huge binomial coefficient (v2)
  • 365 A huge binomial coefficient (v3)
  • 379 Least common multiple count
  • 381 prime-k factorial
  • 381 prime-k factorial (v2)
  • 387 Harshad Numbers
  • 401 Sum of squares of divisors
  • 401 Sum of squares of divisors (v2)
  • 407 Idempotents
  • 407 Idempotents (v2)
  • 407 Idempotents (v3)
  • 417 Reciprocal cycles II
  • 425 Prime connection
  • 429 Sum of squares of unitary divisors
  • 435 Polynomials of Fibonacci numbers
  • 435 Polynomials of Fibonacci numbers (v2)
  • 443 GCD sequence
  • 451 Modular inverses
  • 451 Modular inverses (v2)
  • 479 Roots on the Rise
  • 485 Maximum number of divisors
  • 487 Sums of power sums
  • 487 Sums of power sums (v2)
  • 500 Problem 500
  • 501 Eight Divisors
  • 512 Sums of totients of powers
  • 516 5-smooth totients
  • 516 5-smooth totients (v2)
  • 518 Prime Triples and Geometric Sequences
  • 521 Smallest prime factor
  • 521 Smallest prime factor (v2)
  • 521 Smallest prime factor (v3)
  • 531 Chinese leftovers
  • 545 Faulhaber's Formulas
  • 545 Faulhaber's Formulas (v2)
  • 549 Divisibility of factorials
  • 565 Divisibility of sum of divisors
  • 571 Super Pandigital Numbers
  • 571 Super Pandigital Numbers (v2)
  • 581 47-smooth triangular numbers
  • 601 Divisibility streaks
  • 601 Divisibility streaks (v2)
  • 609 pi sequences
  • 618 Numbers with a given prime factor sum
  • 621 Expressing an integer as the sum of triangular numbers
  • 622 Riffle Shuffles
  • 622 Riffle Shuffles (v2)
  • 625 Gcd sum
  • 634 Numbers of the form a^2b^3
  • 634 Numbers of the form a^2b^3 (v2)
  • 642 Sum of largest prime factors
  • 642 Sum of largest prime factors (v2)
  • 650 Divisors of Binomial Product
  • 650 Divisors of Binomial Product (v2)
  • 659 Largest prime
  • 668 Square root smooth numbers
  • 675 2 to omega of n
  • 678 Fermat-like Equations
  • 678 Fermat-like Equations (v2)
  • 684 Inverse Digit Sum
  • 686 Powers of Two
  • 688 Piles of Plates
  • 694 Cube-full Divisors
  • 700 Eulercoin
  • 700 Eulercoin (v2)
  • 704 Factors of Two in Binomial Coefficients
  • 708 Twos are all you need
  • 719 Number Splitting
  • 745 Sum of Squares
  • 745 Sum of Squares (v2)
  • 749 Near Power Sums
  • 751 Concatenation Coincidence
  • 752 Powers of 1 + sqrt(7)
  • 754 Product of Gauss Factorials
  • 754 Product of Gauss Factorials (v2)
  • 757 Stealthy Numbers (v2)
  • 784 Reciprocal Pairs (v2)
  • 795 Alternating GCD Sum
  • 800 Hybrid Integers
  • 816 Shortest distance among points
  • 820 Nth Digit of Reciprocals
  • 853 Pisano Periods 1
  • 853 Pisano Periods 1 (v2)
  • 853 Pisano Periods 1 (v3)
  • 854 Pisano Periods 2
  • 932 2025
  • 932 2025 (v2)
  • 952 Order Modulo Factorial
  • 952 Order Modulo Factorial (v2)
• Raku
  • 601 Divisibility streaks
• Sidef
  • 001 Multiples of 3 and 5
  • 001 Multiples of 3 and 5 (v2)
  • 002 Even Fibonacci numbers
  • 003 Largest prime factor
  • 004 Largest palindrome product
  • 005 Smallest multiple
  • 005 Smallest multiple (v2)
  • 006 Sum square difference
  • 006 Sum square difference (v2)
  • 007 10001st prime
  • 007 10001st prime (v2)
  • 007 10001st prime (v3)
  • 008 Largest product in a series
  • 009 Special Pythagorean triplet
  • 009 Special Pythagorean triplet (v2)
  • 010 Summation of primes
  • 010 Summation of primes (v2)
  • 011 Largest product in a grid
  • 011 Largest product in a grid (v2)
  • 012 Highly divisible triangular number
  • 012 Highly divisible triangular number (v2)
  • 013 Large sum
  • 013 Large sum (v2)
  • 014 Longest Collatz sequence
  • 015 Lattice paths
  • 016 Power digit sum
  • 017 Number letter counts
  • 018 Maximum path sum I
  • 019 Counting Sundays
  • 020 Factorial digit sum
  • 021 Amicable numbers
  • 021 Amicable numbers (v2)
  • 022 Names scores
  • 023 Non-abundant sums
  • 024 Lexicographic permutations
  • 024 Lexicographic permutations (v2)
  • 025 1000-digit Fibonacci number
  • 025 1000-digit Fibonacci number (v2)
  • 025 1000-digit Fibonacci number (v3)
  • 026 Reciprocal cycles
  • 027 Quadratic primes
  • 028 Number spiral diagonals
  • 029 Distinct powers
  • 030 Digit fifth powers
  • 031 Coin sums
  • 032 Pandigital products
  • 033 Digit cancelling fractions
  • 034 Digit factorials
  • 035 Circular primes
  • 035 Circular primes (v2)
  • 036 Double-base palindromes
  • 036 Double-base palindromes (v2)
  • 036 Double-base palindromes (v3)
  • 036 Double-base palindromes (v4)
  • 037 Truncatable primes
  • 038 Pandigital multiples
  • 039 Integer right triangles
  • 040 Champernowne's constant
  • 040 Champernowne's constant (v2)
  • 041 Pandigital prime
  • 042 Coded triangle numbers
  • 044 Pentagon numbers
  • 045 Triangular pentagonal and hexagonal
  • 045 Triangular pentagonal and hexagonal (v2)
  • 046 Goldbach's other conjecture
  • 047 Distinct primes factors
  • 047 Distinct primes factors (v2)
  • 048 Self powers
  • 049 Prime permutations
  • 050 Consecutive prime sum
  • 050 Consecutive prime sum (v2)
  • 051 Prime digit replacements
  • 052 Permuted multiples
  • 052 Permuted multiples (v2)
  • 053 Combinatoric selections
  • 055 Lychrel numbers
  • 056 Powerful digit sum
  • 057 Square root convergents
  • 058 Spiral primes
  • 059 XOR decryption
  • 060 Prime pair sets
  • 061 Cyclical figurate numbers
  • 062 Cubic permutations
  • 063 Powerful digit counts
  • 064 Odd period square roots
  • 065 Convergents of e
  • 066 Diophantine equation
  • 067 Maximum path sum II
  • 068 Magic 5-gon ring
  • 069 Totient maximum
  • 070 Totient permutation
  • 070 Totient permutation (v2)
  • 071 Ordered fractions
  • 072 Counting fractions
  • 072 Counting fractions (v2)
  • 073 Counting fractions in a range
  • 075 Singular integer right triangles
  • 075 Singular integer right triangles (v2)
  • 076 Counting summations
  • 077 Prime summations
  • 079 Passcode derivation
  • 079 Passcode derivation (v2)
  • 080 Square root digital expansion
  • 081 Path sum two ways
  • 082 Path sum three ways
  • 085 Counting rectangles
  • 087 Prime power triples
  • 089 Roman numerals
  • 094 Almost equilateral triangles
  • 095 Amicable chains
  • 096 Su Doku
  • 097 Large non-Mersenne prime
  • 099 Largest exponential
  • 100 Arranged probability
  • 100 Arranged probability (v2)
  • 100 Arranged probability (v3)
  • 104 Pandigital Fibonacci ends
  • 108 Diophantine reciprocals I
  • 108 Diophantine reciprocals I (v2)
  • 110 Diophantine reciprocals II
  • 111 Primes with runs
  • 112 Bouncy numbers
  • 119 Digit power sum
  • 120 Square remainders
  • 123 Prime square remainders
  • 124 Ordered radicals
  • 125 Palindromic sums
  • 129 Repunit divisibility
  • 130 Composites with prime repunit property
  • 130 Composites with prime repunit property (v2)
  • 131 Prime cube partnership
  • 132 Large repunit factors
  • 133 Repunit nonfactors
  • 134 Prime pair connection
  • 137 Fibonacci golden nuggets
  • 138 Special isosceles triangles
  • 140 Modified Fibonacci golden nuggets
  • 140 Modified Fibonacci golden nuggets (v2)
  • 142 Perfect Square Collection
  • 169 Exploring the number of different ways a number can be expressed as a sum of powers of 2
  • 169 Exploring the number of different ways a number can be expressed as a sum of powers of 2 (v2)
  • 173 Using up to one million tiles how many different hollow square laminae can be formed
  • 174 Counting the number of hollow square laminae that can form one two three distinct arrangements
  • 182 RSA encryption
  • 183 Maximum product of parts
  • 187 Semiprimes
  • 188 The hyperexponentiation of a number
  • 191 Prize Strings
  • 193 Squarefree Numbers
  • 197 Investigating the behaviour of a recursively defined sequence
  • 203 Squarefree Binomial Coefficients
  • 204 Generalised Hamming Numbers
  • 206 Concealed Square
  • 231 The prime factorisation of binomial coefficients
  • 235 An Arithmetic Geometric sequence
  • 248 Numbers for which Euler's totient function equals 13
  • 271 Modular Cubes part 1
  • 277 A Modified Collatz sequence
  • 293 Pseudo-Fortunate Numbers
  • 345 Matrix Sum
  • 346 Strong Repunits
  • 381 prime-k factorial
  • 387 Harshad Numbers
  • 435 Polynomials of Fibonacci numbers
  • 443 GCD sequence
  • 463 A weird recurrence relation
  • 479 Roots on the Rise
  • 493 Under the Rainbow
  • 500 Problem 500
  • 501 Eight Divisors
  • 501 Eight Divisors (v2)
  • 518 Prime Triples and Geometric Sequences
  • 521 Smallest prime factor
  • 581 47-smooth triangular numbers
  • 601 Divisibility streaks
  • 622 Riffle Shuffles
  • 634 Numbers of the form a^2b^3
  • 642 Sum of largest prime factors
  • 668 Square root smooth numbers
  • 684 Inverse Digit Sum
  • 684 Inverse Digit Sum (v2)
  • 686 Powers of Two
  • 686 Powers of Two (v2)
  • 688 Piles of Plates
  • 694 Cube-full Divisors
  • 700 Eulercoin
  • 704 Factors of Two in Binomial Coefficients
  • 708 Twos are all you need
  • 708 Twos are all you need (v2)
  • 745 Sum of Squares
  • 745 Sum of Squares (v2)
  • 748 Upside down Diophantine equation
  • 751 Concatenation Coincidence
  • 752 Powers of 1 + sqrt(7)
  • 784 Reciprocal Pairs
  • 800 Hybrid Integers
  • 808 Reversible prime squares
  • 816 Shortest distance among points
  • 836 A Bold Proposition
  • 853 Pisano Periods 1
  • 854 Pisano Periods 2
  • 854 Pisano Periods 2 (v2)
  • 918 Recursive Sequence Summation
  • 932 2025