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Problems


IDDescription / TitleSolved By
101
Investigate the optimum polynomial function to model the first k terms of a given sequence.
4015
102
For how many triangles in the text file does the interior contain the origin?
8923
103
Investigating sets with a special subset sum property.
3003
104
Finding Fibonacci numbers for which the first and last nine digits are pandigital.
6726
105
Find the sum of the special sum sets in the file.
3028
106
Find the minimum number of comparisons needed to identify special sum sets.
2413
107
Determining the most efficient way to connect the network.
4289
108
Solving the Diophantine equation 1/x + 1/y = 1/n.
5639
109
How many distinct ways can a player checkout in the game of darts with a score of less than 100?
3023
110
Find an efficient algorithm to analyse the number of solutions of the equation 1/x + 1/y = 1/n.
3516
111
Search for 10-digit primes containing the maximum number of repeated digits.
2870
112
Investigating the density of "bouncy" numbers.
9988
113
How many numbers below a googol (10100) are not "bouncy"?
4818
114
Investigating the number of ways to fill a row with separated blocks that are at least three units long.
4315
115
Finding a generalisation for the number of ways to fill a row with separated blocks.
3938
116
Investigating the number of ways of replacing square tiles with one of three coloured tiles.
4753
117
Investigating the number of ways of tiling a row using different-sized tiles.
4392
118
Exploring the number of ways in which sets containing prime elements can be made.
2588
119
Investigating the numbers which are equal to sum of their digits raised to some power.
4828
120
Finding the maximum remainder when (a − 1)n + (a + 1)n is divided by a2.
5857
121
Investigate the game of chance involving coloured discs.
3768
122
Finding the most efficient exponentiation method.
3134
123
Determining the remainder when (pn − 1)n + (pn + 1)n is divided by pn2.
5024
124
Determining the kth element of the sorted radical function.
6248
125
Finding square sums that are palindromic.
5857
126
Exploring the number of cubes required to cover every visible face on a cuboid.
1729
127
Investigating the number of abc-hits below a given limit.
2300
128
Which tiles in the hexagonal arrangement have prime differences with neighbours?
1899
129
Investigating minimal repunits that divide by n.
2548
130
Finding composite values, n, for which n−1 is divisible by the length of the smallest repunits that divide it.
2413
131
Determining primes, p, for which n3 + n2p is a perfect cube.
3091
132
Determining the first forty prime factors of a very large repunit.
2689
133
Investigating which primes will never divide a repunit containing 10n digits.
2319
134
Finding the smallest positive integer related to any pair of consecutive primes.
2831
135
Determining the number of solutions of the equation x2 − y2 − z2 = n.
2568
136
Discover when the equation x2 − y2 − z2 = n has a unique solution.
2290
137
Determining the value of infinite polynomial series for which the coefficients are Fibonacci numbers.
2187
138
Investigating isosceles triangle for which the height and base length differ by one.
2455
139
Finding Pythagorean triangles which allow the square on the hypotenuse to be tiled.
2223
140
Investigating the value of infinite polynomial series for which the coefficients are a linear second order recurrence relation.
1708
141
Investigating progressive numbers, n, which are also square.
1479
142
Perfect Square Collection
2430
143
Investigating the Torricelli point of a triangle
1081
144
Investigating multiple reflections of a laser beam.
2126
145
How many reversible numbers are there below one-billion?
7029
146
Investigating a Prime Pattern
2061
147
Rectangles in cross-hatched grids
1196
148
Exploring Pascal's triangle.
2190
149
Searching for a maximum-sum subsequence.
1967
150
Searching a triangular array for a sub-triangle having minimum-sum.
1604