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