
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 
208 
Robot Walks 
70% 

November 11, 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 
216 
Investigating the primality of numbers ... 
45% 

November 1, 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 
237 
Tours on a 4 x n playing board 
70% 

October 17, 2017 
yes 
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 
248 
Numbers for which Euler's totient function ... 
70% 

November 12, 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 
279 
Triangles with integral sides and an integral ... 
60% 

December 27, 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 
288 
An enormous factorial 
35% 

October 19, 2017 
yes 
290 
Digital Signature 
50% 

November 14, 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 
308 
An amazing Primegenerating Automaton 
65% 

December 11, 2017 
yes 
309 
Integer Ladders 
50% 

July 27, 2017 
yes 
310 
Nim Square 
40% 

December 12, 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 
324 
Building a tower 
50% 

December 20, 2017 
yes 
327 
Rooms of Doom 
40% 

October 27, 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 
358 
Cyclic numbers 
25% 

October 26, 2017 
no 
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 
375 
Minimum of subsequences 
40% 

December 6, 2017 
yes 
381 
(primek) factorial 
15% 

August 20, 2017 
yes 
386 
Maximum length of an antichain 
40% 

November 3, 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 
458 
Permutations of Project 
30% 

December 18, 2017 
yes 
461 
Almost Pi 
30% 

September 28, 2017 
yes 
473 
Phigital number base 
35% 

September 30, 2017 
yes 
485 
Maximum number of divisors 
30% 

December 8, 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 
516 
5smooth totients 
20% 

November 15, 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 
565 
Divisibility of sum of divisors 
35% 

December 10, 2017 
yes 
571 
Super Pandigital Numbers 
25% 

September 22, 2017 
yes 
577 
Counting hexagons 
20% 

December 31, 2017 
yes 
581 
47smooth triangular numbers 
25% 

October 12, 2017 
yes 
587 
Concave triangle 
20% 

October 23, 2017 
yes 
601 
Divisibility streaks 
20% 

October 10, 2017 
yes 
607 
Marsh Crossing 


October 18, 2017 
no 
610 
Roman Numerals II 


October 9, 2017 
no 
611 
Hallway of square steps 


October 10, 2017 
yes 
613 
Pythagorean Ant 


November 21, 2017 
no 
615 
The millionth number with at least one ... 


December 4, 2017 
no 