
problem 
difficulty 
solved 
live test 
1 
Multiples of 3 and 5 
5% 
easy 
February 22, 2017 
yes 
2 
Even Fibonacci numbers 
5% 
easy 
February 23, 2017 
yes 
3 
Largest prime factor 
5% 
easy 
February 23, 2017 
yes 
4 
Largest palindrome product 
5% 
medium 
February 23, 2017 
yes 
5 
Smallest multiple 
5% 
medium 
February 23, 2017 
yes 
6 
Sum square difference 
5% 
easy 
February 23, 2017 
yes 
7 
10001st prime 
5% 
easy 
February 23, 2017 
yes 
8 
Largest product in a series 
5% 
easy 
February 23, 2017 
yes 
9 
Special Pythagorean triplet 
5% 
easy 
February 23, 2017 
yes 
10 
Summation of primes 
5% 
medium 
February 23, 2017 
yes 
11 
Largest product in a grid 
5% 
easy 
February 23, 2017 
yes 
12 
Highly divisible triangular number 
5% 
easy 
February 23, 2017 
yes 
13 
Large sum 
5% 
easy 
February 23, 2017 
yes 
14 
Longest Collatz sequence 
5% 
easy 
February 23, 2017 
yes 
15 
Lattice paths 
5% 
easy 
February 23, 2017 
yes 
16 
Power digit sum 
5% 
easy 
February 23, 2017 
yes 
17 
Number letter counts 
5% 
easy 
February 24, 2017 
yes 
18 
Maximum path sum I 
5% 
easy 
February 24, 2017 
yes 
19 
Counting Sundays 
5% 
easy 
February 24, 2017 
yes 
20 
Factorial digit sum 
5% 
easy 
February 24, 2017 
yes 
21 
Amicable numbers 
5% 
easy 
February 24, 2017 
yes 
22 
Names scores 
5% 
easy 
February 23, 2017 
no 
23 
Nonabundant sums 
5% 
easy 
February 24, 2017 
yes 
24 
Lexicographic permutations 
5% 
easy 
February 23, 2017 
yes 
25 
1000digit Fibonacci number 
5% 
easy 
February 24, 2017 
yes 
26 
Reciprocal cycles 
5% 
easy 
February 24, 2017 
yes 
27 
Quadratic primes 
5% 
easy 
February 23, 2017 
yes 
28 
Number spiral diagonals 
5% 
easy 
February 23, 2017 
yes 
29 
Distinct powers 
5% 
easy 
February 24, 2017 
yes 
30 
Digit fifth powers 
5% 
easy 
February 23, 2017 
yes 
31 
Coin sums 
5% 
easy 
February 23, 2017 
yes 
32 
Pandigital products 
5% 
easy 
February 23, 2017 
yes 
33 
Digit cancelling fractions 
5% 
hard 
February 24, 2017 
yes 
34 
Digit factorials 
5% 
easy 
February 23, 2017 
yes 
35 
Circular primes 
5% 
easy 
February 24, 2017 
yes 
36 
Doublebase palindromes 
5% 
easy 
February 24, 2017 
yes 
37 
Truncatable primes 
5% 
easy 
February 23, 2017 
yes 
38 
Pandigital multiples 
5% 
easy 
February 25, 2017 
yes 
39 
Integer right triangles 
5% 
easy 
February 25, 2017 
yes 
40 
Champernowne's constant 
5% 
medium 
February 25, 2017 
yes 
41 
Pandigital prime 
5% 
easy 
February 25, 2017 
yes 
42 
Coded triangle numbers 
5% 
easy 
February 27, 2017 
yes 
43 
Substring divisibility 
5% 
easy 
February 23, 2017 
yes 
44 
Pentagon numbers 
5% 
easy 
February 27, 2017 
yes 
45 
Triangular, pentagonal, and hexagonal 
5% 
easy 
February 27, 2017 
yes 
46 
Goldbach's other conjecture 
5% 
easy 
February 27, 2017 
yes 
47 
Distinct primes factors 
5% 
easy 
February 26, 2017 
yes 
48 
Self powers 
5% 
easy 
February 26, 2017 
yes 
49 
Prime permutations 
5% 
hard 
February 27, 2017 
yes 
50 
Consecutive prime sum 
5% 
hard 
February 27, 2017 
yes 
51 
Prime digit replacements 
15% 
advanced 
February 27, 2017 
yes 
52 
Permuted multiples 
5% 
easy 
February 27, 2017 
yes 
53 
Combinatoric selections 
5% 
easy 
February 27, 2017 
yes 
54 
Poker hands 
10% 
easy 
February 28, 2017 
yes 
55 
Lychrel numbers 
5% 
easy 
February 27, 2017 
yes 
56 
Powerful digit sum 
5% 
easy 
February 28, 2017 
yes 
57 
Square root convergents 
5% 
easy 
February 28, 2017 
yes 
58 
Spiral primes 
5% 
easy 
February 28, 2017 
yes 
59 
XOR decryption 
5% 
easy 
March 1, 2017 
yes 
60 
Prime pair sets 
20% 
hard 
March 1, 2017 
yes 
61 
Cyclical figurate numbers 
20% 
easy 
March 6, 2017 
yes 
62 
Cubic permutations 
15% 
easy 
March 1, 2017 
yes 
63 
Powerful digit counts 
5% 
easy 
February 28, 2017 
yes 
64 
Odd period square roots 
20% 
easy 
March 8, 2017 
yes 
65 
Convergents of e 
15% 
easy 
March 8, 2017 
yes 
66 
Diophantine equation 
25% 
hard 
March 12, 2017 
yes 
67 
Maximum path sum II 
5% 
medium 
February 24, 2017 
yes 
68 
Magic 5gon ring 
25% 
hard 
March 13, 2017 
yes 
69 
Totient maximum 
10% 
easy 
March 1, 2017 
yes 
70 
Totient permutation 
20% 
easy 
March 11, 2017 
yes 
71 
Ordered fractions 
10% 
easy 
March 13, 2017 
yes 
72 
Counting fractions 
20% 
easy 
March 13, 2017 
yes 
73 
Counting fractions in a range 
15% 
easy 
March 15, 2017 
yes 
74 
Digit factorial chains 
15% 
easy 
March 12, 2017 
yes 
75 
Singular integer right triangles 
25% 
easy 
March 12, 2017 
yes 
76 
Counting summations 
10% 
easy 
March 13, 2017 
yes 
77 
Prime summations 
25% 
easy 
March 17, 2017 
yes 
78 
Coin partitions 
30% 
medium 
March 16, 2017 
yes 
79 
Passcode derivation 
5% 
easy 
March 13, 2017 
yes 
80 
Square root digital expansion 
20% 
easy 
March 14, 2017 
yes 
81 
Path sum: two ways 
10% 
easy 
March 12, 2017 
yes 
82 
Path sum: three ways 
20% 
easy 
March 12, 2017 
yes 
83 
Path sum: four ways 
25% 
hard 
March 12, 2017 
yes 
84 
Monopoly odds 
35% 
hard 
March 17, 2017 
yes 
85 
Counting rectangles 
15% 
medium 
March 12, 2017 
yes 
86 
Cuboid route 
35% 
hard 
March 15, 2017 
yes 
87 
Prime power triples 
20% 
easy 
March 12, 2017 
yes 
88 
Productsum numbers 
40% 
easy 
March 19, 2017 
yes 
89 
Roman numerals 
20% 
easy 
March 15, 2017 
yes 
90 
Cube digit pairs 
40% 
easy 
March 19, 2017 
yes 
91 
Right triangles with integer coordinates 
25% 
medium 
March 15, 2017 
yes 
92 
Square digit chains 
5% 
easy 
March 9, 2017 
yes 
93 
Arithmetic expressions 
15% 
medium 
March 16, 2017 
yes 
94 
Almost equilateral triangles 
35% 
medium 
March 16, 2017 
yes 
95 
Amicable chains 
30% 
medium 
March 16, 2017 
yes 
96 
Su Doku 
25% 
hard 
March 13, 2017 
yes 
97 
Large nonMersenne prime 
5% 
hard 
March 2, 2017 
yes 
98 
Anagramic squares 
35% 
hard 
March 14, 2017 
yes 
99 
Largest exponential 
10% 
medium 
March 1, 2017 
yes 
100 
Arranged probability 
30% 
advanced 
March 15, 2017 
yes 
101 
Optimum polynomial 
35% 

May 23, 2017 
yes 
102 
Triangle containment 
15% 
easy 
May 11, 2017 
yes 
103 
Special subset sums: optimum 
45% 
easy 
May 16, 2017 
yes 
104 
Pandigital Fibonacci ends 
25% 
easy 
May 12, 2017 
yes 
105 
Special subset sums: testing 
45% 
easy 
May 16, 2017 
yes 
106 
Special subset sums: metatesting 
50% 

August 8, 2017 
yes 
107 
Minimal network 
35% 
easy 
May 11, 2017 
no 
108 
Diophantine reciprocals I 
30% 
easy 
May 12, 2017 
yes 
109 
Darts 
45% 

May 17, 2017 
yes 
110 
Diophantine reciprocals II 
40% 
easy 
July 28, 2017 
yes 
111 
Primes with runs 
45% 
easy 
May 17, 2017 
yes 
112 
Bouncy numbers 
15% 
advanced 
May 11, 2017 
yes 
113 
Nonbouncy numbers 
30% 
easy 
May 15, 2017 
yes 
114 
Counting block combinations I 
35% 
medium 
May 13, 2017 
yes 
115 
Counting block combinations II 
35% 
medium 
May 13, 2017 
yes 
116 
Red, green or blue tiles 
30% 
medium 
May 14, 2017 
yes 
117 
Red, green, and blue tiles 
35% 
easy 
May 18, 2017 
yes 
118 
Pandigital prime sets 
45% 
hard 
May 18, 2017 
yes 
119 
Digit power sum 
30% 
easy 
May 13, 2017 
yes 
120 
Square remainders 
25% 
easy 
May 11, 2017 
no 
121 
Disc game prize fund 
35% 
easy 
May 19, 2017 
yes 
122 
Efficient exponentiation 
40% 
easy 
May 15, 2017 
yes 
123 
Prime square remainders 
30% 

May 11, 2017 
no 
124 
Ordered radicals 
25% 
advanced 
May 19, 2017 
yes 
125 
Palindromic sums 
25% 
easy 
May 17, 2017 
yes 
126 
Cuboid layers 
55% 

August 18, 2017 
yes 
127 
abchits 
50% 

June 26, 2017 
yes 
128 
Hexagonal tile differences 
55% 
hard 
June 24, 2017 
yes 
129 
Repunit divisibility 
45% 
hard 
May 21, 2017 
yes 
130 
Composites with prime repunit property 
45% 
easy 
July 17, 2017 
yes 
131 
Prime cube partnership 
40% 
hard 
June 27, 2017 
yes 
132 
Large repunit factors 
45% 

June 1, 2017 
yes 
133 
Repunit nonfactors 
50% 
medium 
June 2, 2017 
yes 
134 
Prime pair connection 
45% 

May 24, 2017 
no 
135 
Same differences 
45% 
medium 
May 19, 2017 
yes 
136 
Singleton differences 
45% 

May 19, 2017 
no 
137 
Fibonacci golden nuggets 
50% 
easy 
August 1, 2017 
yes 
138 
Special isosceles triangles 
45% 
easy 
July 10, 2017 
yes 
139 
Pythagorean tiles 
50% 

June 1, 2017 
yes 
141 
Investigating progressive numbers, n, ... 
60% 

September 1, 2017 
yes 
142 
Perfect Square Collection 
45% 

June 27, 2017 
no 
144 
Investigating multiple reflections of ... 
50% 

June 30, 2017 
no 
145 
How many reversible numbers are there ... 
20% 

May 23, 2017 
no 
146 
Investigating a Prime Pattern 
50% 
easy 
June 16, 2017 
yes 
147 
Rectangles in crosshatched grids 
65% 
hard 
August 9, 2017 
yes 
148 
Exploring Pascal's triangle 
50% 

July 12, 2017 
yes 
149 
Searching for a maximumsum subsequence 
50% 

May 25, 2017 
no 
150 
Searching a triangular array for a sub ... 
55% 
easy 
July 5, 2017 
yes 
151 
Paper sheets of standard sizes: an expected ... 
35% 

May 23, 2017 
no 
152 
Writing 1/2 as a sum of inverse squares 
65% 
advanced 
September 17, 2017 
yes 
154 
Exploring Pascal's pyramid 
60% 
hard 
July 13, 2017 
yes 
155 
Counting Capacitor Circuits 
60% 
easy 
September 15, 2017 
yes 
156 
Counting Digits 
70% 
medium 
October 6, 2017 
yes 
158 
Exploring strings for which only one character ... 
55% 

June 13, 2017 
yes 
159 
Digital root sums of factorisations 
60% 
medium 
June 22, 2017 
no 
160 
Factorial trailing digits 
60% 

July 13, 2017 
yes 
161 
Triominoes 
70% 
hard 
June 29, 2017 
yes 
162 
Hexadecimal numbers 
45% 
medium 
May 25, 2017 
yes 
163 
Crosshatched triangles 
70% 
easy 
July 7, 2017 
yes 
164 
Numbers for which no three consecutive ... 
45% 
easy 
June 16, 2017 
yes 
165 
Intersections 
65% 
easy 
June 20, 2017 
yes 
166 
Criss Cross 
50% 
easy 
June 14, 2017 
yes 
168 
Number Rotations 
65% 
easy 
August 3, 2017 
yes 
169 
Exploring the number of different ways ... 
50% 
easy 
May 30, 2017 
yes 
170 
Find the largest 0 to 9 pandigital that ... 
70% 
easy 
June 19, 2017 
yes 
171 
Finding numbers for which the sum of the ... 
70% 
medium 
July 7, 2017 
yes 
172 
Investigating numbers with few repeated ... 
55% 

June 15, 2017 
yes 
173 
Using up to one million tiles how many ... 
30% 
medium 
May 22, 2017 
yes 
174 
Counting the number of "hollow" square ... 
40% 
easy 
May 23, 2017 
yes 
178 
Step Numbers 
55% 
medium 
June 28, 2017 
yes 
179 
Consecutive positive divisors 
25% 
easy 
May 16, 2017 
yes 
181 
Investigating in how many ways objects ... 
70% 
easy 
June 28, 2017 
yes 
182 
RSA encryption 
60% 

September 3, 2017 
yes 
183 
Maximum product of parts 
45% 
easy 
June 13, 2017 
yes 
185 
Number Mind 
55% 
medium 
May 30, 2017 
yes 
186 
Connectedness of a network 
60% 
easy 
July 4, 2017 
yes 
187 
Semiprimes 
20% 
medium 
May 23, 2017 
yes 
188 
The hyperexponentiation of a number 
35% 

June 14, 2017 
yes 
189 
Tricolouring a triangular grid 
70% 
easy 
September 5, 2017 
yes 
190 
Maximising a weighted product 
50% 

June 27, 2017 
yes 
191 
Prize Strings 
45% 

May 25, 2017 
yes 
193 
Squarefree Numbers 
55% 

June 15, 2017 
yes 
196 
Prime triplets 
65% 

August 19, 2017 
yes 
197 
Investigating the behaviour of a recursively ... 
45% 

June 13, 2017 
no 
199 
Iterative Circle Packing 
70% 

September 10, 2017 
yes 
200 
Find the 200th primeproof sqube containing ... 
65% 

August 26, 2017 
yes 
201 
Subsets with a unique sum 
65% 

July 2, 2017 
yes 
203 
Squarefree Binomial Coefficients 
25% 

May 31, 2017 
yes 
204 
Generalised Hamming Numbers 
30% 

May 27, 2017 
yes 
205 
Dice Game 
15% 

May 26, 2017 
yes 
206 
Concealed Square 
5% 

May 26, 2017 
no 
207 
Integer partition equations 
40% 

May 31, 2017 
yes 
209 
Circular Logic 
60% 

September 12, 2017 
no 
211 
Divisor Square Sum 
50% 

May 31, 2017 
yes 
213 
Flea Circus 
60% 

July 5, 2017 
yes 
214 
Totient Chains 
40% 

June 20, 2017 
yes 
215 
Crackfree Walls 
50% 

July 22, 2017 
yes 
218 
Perfect rightangled triangles 
55% 

August 28, 2017 
no 
219 
Skewcost coding 
70% 

July 30, 2017 
yes 
222 
Sphere Packing 
60% 

July 24, 2017 
yes 
225 
Tribonacci nondivisors 
45% 

June 23, 2017 
yes 
226 
A Scoop of Blancmange 
65% 

September 18, 2017 
yes 
227 
The Chase 
65% 

August 24, 2017 
yes 
229 
Four Representations using Squares 
70% 

June 21, 2017 
yes 
230 
Fibonacci Words 
50% 

July 12, 2017 
yes 
231 
The prime factorisation of binomial coefficients 
40% 

June 28, 2017 
yes 
232 
The Race 
65% 

July 21, 2017 
yes 
234 
Semidivisible numbers 
50% 

August 5, 2017 
yes 
235 
An Arithmetic Geometric sequence 
40% 

July 2, 2017 
no 
239 
Twentytwo Foolish Primes 
65% 

September 9, 2017 
yes 
240 
Top Dice 
60% 

July 20, 2017 
yes 
243 
Resilience 
35% 

June 19, 2017 
no 
244 
Sliders 
70% 

September 25, 2017 
yes 
247 
Squares under a hyperbola 
65% 

August 14, 2017 
yes 
249 
Prime Subset Sums 
60% 

July 14, 2017 
yes 
250 
250250 
55% 

July 14, 2017 
yes 
259 
Reachable Numbers 
70% 

July 4, 2017 
yes 
260 
Stone Game 
70% 

August 4, 2017 
yes 
265 
Binary Circles 
40% 

July 1, 2017 
yes 
266 
Pseudo Square Root 
65% 

July 3, 2017 
yes 
267 
Billionaire 
50% 

July 11, 2017 
yes 
268 
Counting numbers with at least four distinct ... 
70% 

September 27, 2017 
yes 
273 
Sum of Squares 
70% 

September 14, 2017 
yes 
274 
Divisibility Multipliers 
65% 

August 23, 2017 
yes 
277 
A Modified Collatz sequence 
35% 

July 11, 2017 
yes 
278 
Linear Combinations of Semiprimes 
50% 

July 11, 2017 
yes 
280 
Ant and seeds 
65% 

August 25, 2017 
yes 
284 
Steady Squares 
55% 

October 13, 2017 
yes 
286 
Scoring probabilities 
50% 

July 6, 2017 
yes 
287 
Quadtree encoding (a simple compression ... 
40% 

August 29, 2017 
yes 
291 
Panaitopol Primes 
45% 

July 7, 2017 
yes 
293 
PseudoFortunate Numbers 
25% 

July 26, 2017 
yes 
297 
Zeckendorf Representation 
35% 

July 25, 2017 
yes 
300 
Protein folding 
50% 

August 27, 2017 
yes 
301 
Nim 
15% 

July 4, 2017 
yes 
303 
Multiples with small digits 
35% 

July 3, 2017 
yes 
304 
Primonacci 
35% 

August 7, 2017 
yes 
306 
Paperstrip Game 
55% 

September 16, 2017 
yes 
307 
Chip Defects 
35% 

August 12, 2017 
yes 
309 
Integer Ladders 
50% 

July 27, 2017 
yes 
313 
Sliding game 
30% 

September 19, 2017 
yes 
315 
Digital root clocks 
20% 

July 29, 2017 
yes 
317 
Firecracker 
35% 

July 5, 2017 
yes 
321 
Swapping Counters 
30% 

August 30, 2017 
yes 
323 
BitwiseOR operations on random integers 
20% 

July 31, 2017 
yes 
329 
Prime Frog 
25% 

August 13, 2017 
yes 
333 
Special partitions 
35% 

September 20, 2017 
yes 
336 
Maximix Arrangements 
25% 

July 15, 2017 
yes 
341 
Golomb's selfdescribing sequence 
45% 

August 15, 2017 
yes 
343 
Fractional Sequences 
35% 

September 29, 2017 
yes 
345 
Matrix Sum 
15% 

July 18, 2017 
no 
346 
Strong Repunits 
15% 

July 9, 2017 
yes 
347 
Largest integer divisible by two primes 
15% 

July 17, 2017 
yes 
348 
Sum of a square and a cube 
25% 

July 23, 2017 
yes 
349 
Langton's ant 
35% 

July 19, 2017 
yes 
351 
Hexagonal orchards 
25% 

September 26, 2017 
yes 
357 
Prime generating integers 
10% 

July 8, 2017 
yes 
359 
Hilbert's New Hotel 
25% 

September 6, 2017 
yes 
363 
Bézier Curves 
35% 

September 7, 2017 
no 
371 
Licence plates 
30% 

September 21, 2017 
yes 
381 
(primek) factorial 
15% 

August 20, 2017 
yes 
387 
Harshad Numbers 
10% 

August 2, 2017 
yes 
393 
Migrating ants 
50% 

September 23, 2017 
yes 
401 
Sum of squares of divisors 
25% 

August 22, 2017 
yes 
407 
Idempotents 
20% 

August 31, 2017 
yes 
411 
Uphill paths 
45% 

October 5, 2017 
yes 
418 
Factorisation triples 
40% 

October 4, 2017 
yes 
425 
Prime connection 
25% 

August 6, 2017 
yes 
429 
Sum of squares of unitary divisors 
20% 

September 13, 2017 
yes 
455 
Powers With Trailing Digits 
40% 

October 1, 2017 
yes 
461 
Almost Pi 
30% 

September 28, 2017 
yes 
473 
Phigital number base 
35% 

September 30, 2017 
yes 
491 
Double pandigital number divisible by 11 
20% 

August 16, 2017 
yes 
493 
Under The Rainbow 
15% 

August 21, 2017 
yes 
500 
Problem 500!!! 
15% 

September 11, 2017 
yes 
501 
Eight Divisors 
40% 

August 17, 2017 
yes 
504 
Square on the Inside 
15% 

August 11, 2017 
yes 
510 
Tangent Circles 
30% 

September 8, 2017 
yes 
518 
Prime triples and geometric sequences 
20% 

September 2, 2017 
yes 
523 
First Sort I 
60% 

September 4, 2017 
yes 
549 
Divisibility of factorials 
10% 

August 10, 2017 
yes 
563 
Robot Welders 
45% 

October 11, 2017 
yes 
571 
Super Pandigital Numbers 
25% 

September 22, 2017 
yes 
581 
47smooth triangular numbers 
25% 

October 12, 2017 
yes 
601 
Divisibility streaks 
20% 

October 10, 2017 
yes 
610 
Roman Numerals II 


October 9, 2017 
no 