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Problems Archives Cache update: 56 minutes Problems Archives The problems archives table shows problems 1 to 651. If you would like to tackle the 10 most recently published problems then go to Recent problems. Click the description/title of the problem to view details and submit your answer. ID Description / Title Solved By 1 Multiples of 3 and 5 834047 2 Even Fibonacci numbers 666765 3 Largest prime factor 476263 4 Largest palindrome product 422115 5 Smallest multiple 428955 6 Sum square difference 431629 7 10001st prime 368958 8 Largest product in a series 309633 9 Special Pythagorean triplet 313806 10 Summation of primes 287277 11 Largest product in a grid 207029 12 Highly divisible triangular number 194069 13 Large sum 199504 14 Longest Collatz sequence 199344 15 Lattice paths 164576 16 Power digit sum 201444 17 Number letter counts 133434 18 Maximum path sum I 127951 19 Counting Sundays 119066 20 Factorial digit sum 175533 21 Amicable numbers 128681 22 Names scores 118542 23 Non-abundant sums 91300 24 Lexicographic permutations 101261 25 1000-digit Fibonacci number 137312 26 Reciprocal cycles 73631 27 Quadratic primes 76722 28 Number spiral diagonals 96208 29 Distinct powers 92388 30 Digit fifth powers 96765 31 Coin sums 74310 32 Pandigital products 62296 33 Digit cancelling fractions 62955 34 Digit factorials 82985 35 Circular primes 74645 36 Double-base palindromes 78643 37 Truncatable primes 64627 38 Pandigital multiples 55119 39 Integer right triangles 64132 40 Champernowne's constant 70528 41 Pandigital prime 59723 42 Coded triangle numbers 65704 43 Sub-string divisibility 52160 44 Pentagon numbers 50757 45 Triangular, pentagonal, and hexagonal 62652 46 Goldbach's other conjecture 53607 47 Distinct primes factors 50539 48 Self powers 100136 49 Prime permutations 50577 50 Consecutive prime sum 54478 Cache update: 56 minutes Problems Archives The problems archives table shows problems 1 to 651. If you would like to tackle the 10 most recently published problems then go to Recent problems. Click the description/title of the problem to view details and submit your answer. ID Description / Title Solved By 51 Prime digit replacements 28822 52 Permuted multiples 57402 53 Combinatoric selections 51768 54 Poker hands 30867 55 Lychrel numbers 47121 56 Powerful digit sum 51088 57 Square root convergents 35948 58 Spiral primes 34809 59 XOR decryption 36251 60 Prime pair sets 22552 61 Cyclical figurate numbers 21794 62 Cubic permutations 26914 63 Powerful digit counts 37547 64 Odd period square roots 18899 65 Convergents of e 25938 66 Diophantine equation 16775 67 Maximum path sum II 85468 68 Magic 5-gon ring 17742 69 Totient maximum 29739 70 Totient permutation 19113 71 Ordered fractions 25195 72 Counting fractions 19153 73 Counting fractions in a range 21716 74 Digit factorial chains 23059 75 Singular integer right triangles 15286 76 Counting summations 24723 77 Prime summations 16279 78 Coin partitions 14319 79 Passcode derivation 36764 80 Square root digital expansion 17088 81 Path sum: two ways 30119 82 Path sum: three ways 18259 83 Path sum: four ways 15603 84 Monopoly odds 10659 85 Counting rectangles 21401 86 Cuboid route 10756 87 Prime power triples 17949 88 Product-sum numbers 8370 89 Roman numerals 18602 90 Cube digit pairs 9418 91 Right triangles with integer coordinates 13197 92 Square digit chains 36657 93 Arithmetic expressions 9885 94 Almost equilateral triangles 10340 95 Amicable chains 12064 96 Su Doku 14508 97 Large non-Mersenne prime 38688 98 Anagramic squares 9542 99 Largest exponential 26554 100 Arranged probability 13741 Cache update: 56 minutes Problems Archives The problems archives table shows problems 1 to 651. If you would like to tackle the 10 most recently published problems then go to Recent problems. Click the description/title of the problem to view details and submit your answer. ID Description / Title Solved By 101 Optimum polynomial 9519 102 Triangle containment 18888 103 Special subset sums: optimum 6678 104 Pandigital Fibonacci ends 14003 105 Special subset sums: testing 6677 106 Special subset sums: meta-testing 5311 107 Minimal network 9394 108 Diophantine reciprocals I 10921 109 Darts 6842 110 Diophantine reciprocals II 6875 111 Primes with runs 6047 112 Bouncy numbers 21357 113 Non-bouncy numbers 9490 114 Counting block combinations I 9229 115 Counting block combinations II 8436 116 Red, green or blue tiles 10339 117 Red, green, and blue tiles 9481 118 Pandigital prime sets 5773 119 Digit power sum 10568 120 Square remainders 11959 121 Disc game prize fund 8301 122 Efficient exponentiation 6563 123 Prime square remainders 9938 124 Ordered radicals 11939 125 Palindromic sums 11692 126 Cuboid layers 3884 127 abc-hits 5194 128 Hexagonal tile differences 4143 129 Repunit divisibility 5303 130 Composites with prime repunit property 4991 131 Prime cube partnership 6254 132 Large repunit factors 5364 133 Repunit nonfactors 4636 134 Prime pair connection 5908 135 Same differences 5369 136 Singleton difference 4708 137 Fibonacci golden nuggets 4555 138 Special isosceles triangles 4879 139 Pythagorean tiles 4702 140 Modified Fibonacci golden nuggets 3561 141 Investigating progressive numbers, n, which are also square 3201 142 Perfect Square Collection 4923 143 Investigating the Torricelli point of a triangle 2207 144 Investigating multiple reflections of a laser beam 5231 145 How many reversible numbers are there below one-billion? 14357 146 Investigating a Prime Pattern 4196 147 Rectangles in cross-hatched grids 2470 148 Exploring Pascal's triangle 4309 149 Searching for a maximum-sum subsequence 4076 150 Searching a triangular array for a sub-triangle having minimum-sum 3323 Cache update: 55 minutes Problems Archives The problems archives table shows problems 1 to 651. If you would like to tackle the 10 most recently published problems then go to Recent problems. Click the description/title of the problem to view details and submit your answer. ID Description / Title Solved By 151 Paper sheets of standard sizes: an expected-value problem 4617 152 Writing 1/2 as a sum of inverse squares 2151 153 Investigating Gaussian Integers 2113 154 Exploring Pascal's pyramid 2147 155 Counting Capacitor Circuits 2957 156 Counting Digits 1950 1 1 p 157 Solving the diophantine equation /a+ /b= /10n 2190 Exploring strings for which only one character comes lexicographically after its 158 3012 neighbour to the left 159 Digital root sums of factorisations 2719 160 Factorial trailing digits 2869 161 Triominoes 1686 162 Hexadecimal numbers 4575 163 Cross-hatched triangles 1475 164 Numbers for which no three consecutive digits have a sum greater than a given value 4855 165 Intersections 2128 166 Criss Cross 3386 167 Investigating Ulam sequences 1371 168 Number Rotations 2185 Exploring the number of different ways a number can be expressed as a sum of 169 4279 powers of 2 170 Find the largest 0 to 9 pandigital that can be formed by concatenating products 1597 171 Finding numbers for which the sum of the squares of the digits is a square 2260 172 Investigating numbers with few repeated digits 3162 173 Using up to one million tiles how many different "hollow" square laminae can be 7894 formed? Counting the number of "hollow" square laminae that can form one, two, three, ... 174 5046 distinct arrangements Fractions involving the number of different ways a number can be expressed as a sum 175 1459 of powers of 2 176 Right-angled triangles that share a cathetus 1561 177 Integer angled Quadrilaterals 1018 178 Step Numbers 2797 179 Consecutive positive divisors 9732 180 Rational zeros of a function of three variables 1273 181 Investigating in how many ways objects of two different colours can be grouped 1632 182 RSA encryption 2176 183 Maximum product of parts 4005 184 Triangles containing the origin 1303 185 Number Mind 2597 186 Connectedness of a network 2373 187 Semiprimes 9719 188 The hyperexponentiation of a number 5558 189 Tri-colouring a triangular grid 1695 190 Maximising a weighted product 3537 191 Prize Strings 6077 192 Best Approximations 1292 193 Squarefree Numbers 2709 194 Coloured Configurations 1124 195 Inscribed circles of triangles with one angle of 60 degrees 1100 196 Prime triplets 2096 197 Investigating the behaviour of a recursively defined sequence 4258 198 Ambiguous Numbers 890 199 Iterative Circle Packing 1561 200 Find the 200th prime-proof sqube containing the contiguous sub-string "200" 1918 .
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