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Problems Archives

The problems archives table shows problems 1 to 699. 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
4975
152Writing 1/2 as a sum of inverse squares
2364
153Investigating Gaussian Integers
2302
154Exploring Pascal's pyramid
2330
155Counting Capacitor Circuits
3189
156Counting Digits
2140
157Solving the diophantine equation 1/a+1/b= p/10n
2373
158Exploring strings for which only one character comes lexicographically after its neighbour to the left
3245
159Digital root sums of factorisations
2929
160Factorial trailing digits
3098
161Triominoes
1839
162Hexadecimal numbers
4857
163Cross-hatched triangles
1588
164Numbers for which no three consecutive digits have a sum greater than a given value
5203
165Intersections
2286
166Criss Cross
3631
167Investigating Ulam sequences
1480
168Number Rotations
2354
169Exploring the number of different ways a number can be expressed as a sum of powers of 2
4553
170Find the largest 0 to 9 pandigital that can be formed by concatenating products
1744
171Finding numbers for which the sum of the squares of the digits is a square
2447
172Investigating numbers with few repeated digits
3383
173Using up to one million tiles how many different "hollow" square laminae can be formed?
8382
174Counting the number of "hollow" square laminae that can form one, two, three, ... distinct arrangements
5352
175Fractions involving the number of different ways a number can be expressed as a sum of powers of 2
1564
176Right-angled triangles that share a cathetus
1679
177Integer angled Quadrilaterals
1109
178Step Numbers
3033
179Consecutive positive divisors
10364
180Rational zeros of a function of three variables
1397
181Investigating in how many ways objects of two different colours can be grouped
1761
182RSA encryption
2347
183Maximum product of parts
4251
184Triangles containing the origin
1437
185Number Mind
2794
186Connectedness of a network
2556
187Semiprimes
10287
188The hyperexponentiation of a number
5866
189Tri-colouring a triangular grid
1825
190Maximising a weighted product
3766
191Prize Strings
6450
192Best Approximations
1405
193Squarefree Numbers
2913
194Coloured Configurations
1227
195Inscribed circles of triangles with one angle of 60 degrees
1208
196Prime triplets
2263
197Investigating the behaviour of a recursively defined sequence
4501
198Ambiguous Numbers
980
199Iterative Circle Packing
1699
200Find the 200th prime-proof sqube containing the contiguous sub-string "200"
2084