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Problems Archives

The problems archives table shows problems 1 to 667. 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.


IDDescription / TitleSolved By
151Paper sheets of standard sizes: an expected-value problem
4736
152Writing 1/2 as a sum of inverse squares
2211
153Investigating Gaussian Integers
2173
154Exploring Pascal's pyramid
2206
155Counting Capacitor Circuits
3034
156Counting Digits
2008
157Solving the diophantine equation 1/a+1/b= p/10n
2249
158Exploring strings for which only one character comes lexicographically after its neighbour to the left
3088
159Digital root sums of factorisations
2792
160Factorial trailing digits
2954
161Triominoes
1742
162Hexadecimal numbers
4661
163Cross-hatched triangles
1517
164Numbers for which no three consecutive digits have a sum greater than a given value
4962
165Intersections
2179
166Criss Cross
3469
167Investigating Ulam sequences
1408
168Number Rotations
2242
169Exploring the number of different ways a number can be expressed as a sum of powers of 2
4373
170Find the largest 0 to 9 pandigital that can be formed by concatenating products
1639
171Finding numbers for which the sum of the squares of the digits is a square
2333
172Investigating numbers with few repeated digits
3243
173Using up to one million tiles how many different "hollow" square laminae can be formed?
8069
174Counting the number of "hollow" square laminae that can form one, two, three, ... distinct arrangements
5155
175Fractions involving the number of different ways a number can be expressed as a sum of powers of 2
1495
176Right-angled triangles that share a cathetus
1613
177Integer angled Quadrilaterals
1052
178Step Numbers
2887
179Consecutive positive divisors
9939
180Rational zeros of a function of three variables
1318
181Investigating in how many ways objects of two different colours can be grouped
1674
182RSA encryption
2242
183Maximum product of parts
4096
184Triangles containing the origin
1347
185Number Mind
2660
186Connectedness of a network
2434
187Semiprimes
9910
188The hyperexponentiation of a number
5660
189Tri-colouring a triangular grid
1748
190Maximising a weighted product
3616
191Prize Strings
6197
192Best Approximations
1338
193Squarefree Numbers
2786
194Coloured Configurations
1163
195Inscribed circles of triangles with one angle of 60 degrees
1146
196Prime triplets
2155
197Investigating the behaviour of a recursively defined sequence
4343
198Ambiguous Numbers
929
199Iterative Circle Packing
1617
200Find the 200th prime-proof sqube containing the contiguous sub-string "200"
1980