ID
Title
Solved by
Difficulty
1
Multiples of 3 or 5
968630
5%
2
Even Fibonacci numbers
772730
5%
3
Largest prime factor
556069
5%
6
Sum square difference
498564
5%
5
Smallest multiple
495549
5%
4
Largest palindrome product
492178
5%
7
10001st prime
426858
5%
9
Special Pythagorean triplet
362853
5%
8
Largest product in a series
357805
5%
10
Summation of primes
332577
5%
11
Largest product in a grid
238908
5%
16
Power digit sum
233303
5%
14
Longest Collatz sequence
231075
5%
13
Large sum
230801
5%
12
Highly divisible triangular number
225493
5%
20
Factorial digit sum
202010
5%
15
Lattice paths
190748
5%
25
1000-digit Fibonacci number
158637
5%
17
Number letter counts
154837
5%
21
Amicable numbers
149538
5%
18
Maximum path sum I
148231
5%
19
Counting Sundays
137720
5%
22
Names scores
137531
5%
24
Lexicographic permutations
117285
5%
48
Self powers
114337
5%
30
Digit fifth powers
112482
5%
28
Number spiral diagonals
110459
5%
29
Distinct powers
107885
5%
23
Non-abundant sums
106742
5%
67
Maximum path sum II
97707
5%
34
Digit factorials
96375
5%
36
Double-base palindromes
90805
5%
27
Quadratic primes
89543
5%
31
Coin sums
87177
5%
35
Circular primes
86642
5%
26
Reciprocal cycles
86089
5%
40
Champernowne's constant
81935
5%
42
Coded triangle numbers
76092
5%
37
Truncatable primes
75315
5%
39
Integer right triangles
74942
5%
33
Digit cancelling fractions
73468
5%
32
Pandigital products
73072
5%
45
Triangular, pentagonal, and hexagonal
72550
5%
41
Pandigital prime
69753
5%
52
Permuted multiples
66623
5%
38
Pandigital multiples
64591
5%
50
Consecutive prime sum
63927
5%
46
Goldbach's other conjecture
63139
5%
43
Sub-string divisibility
61345
5%
53
Combinatoric selections
60220
5%
44
Pentagon numbers
60009
5%
56
Powerful digit sum
59427
5%
47
Distinct primes factors
59419
5%
49
Prime permutations
59316
5%
55
Lychrel numbers
55012
5%
63
Powerful digit counts
44173
5%
97
Large non-Mersenne prime
43921
5%
57
Square root convergents
42641
5%
92
Square digit chains
42351
5%
59
XOR decryption
42195
5%
79
Passcode derivation
41738
5%
58
Spiral primes
41192
5%
206
Concealed Square
24662
5%
686
Powers of Two
2962
5%
700
Eulercoin
2662
5%
719
Number Splitting
2566
5%
684
Inverse Digit Sum
2320
5%
751
Concatenation Coincidence
1550
5%
54
Poker hands
37000
10%
69
Totient maximum
35633
10%
81
Path sum: two ways
34967
10%
99
Largest exponential
31147
10%
71
Ordered fractions
29951
10%
76
Counting summations
29152
10%
357
Prime generating integers
8119
10%
387
Harshad Numbers
4680
10%
650
Divisors of Binomial Product
1535
10%
757
Stealthy Numbers
832
10%
745
Sum of Squares II
825
10%
51
Prime digit replacements
34812
15%
62
Cubic permutations
32241
15%
65
Convergents of e
30570
15%
74
Digit factorial chains
27340
15%
73
Counting fractions in a range
25566
15%
85
Counting rectangles
25180
15%
112
Bouncy numbers
24989
15%
102
Triangle containment
22343
15%
345
Matrix Sum
5657
15%
347
Largest integer divisible by two primes
4550
15%
346
Strong Repunits
4308
15%
381
(prime-k) factorial
4196
15%
500
Problem 500!!!
3943
15%
549
Divisibility of factorials
2655
15%
622
Riffle Shuffles
1661
15%
694
Cube-full Divisors
856
15%
749
Near Power Sums
541
15%
60
Prime pair sets
27411
20%
61
Cyclical figurate numbers
26153
20%
72
Counting fractions
22856
20%
70
Totient permutation
22788
20%
64
Odd period square roots
22683
20%
89
Roman numerals
21569
20%
82
Path sum: three ways
21526
20%
87
Prime power triples
21310
20%
80
Square root digital expansion
20249
20%
145
How many reversible numbers are there below one-billion?
16827
20%
429
Sum of squares of unitary divisors
2495
20%
407
Idempotents
2411
20%
601
Divisibility streaks
1966
20%
516
5-smooth totients
1535
20%
618
Numbers with a given prime factor sum
985
20%
668
Square root smooth Numbers
961
20%
609
π sequences
892
20%
659
Largest prime
847
20%
704
Factors of Two in Binomial Coefficients
787
20%
688
Piles of Plates
672
20%
754
Product of Gauss Factorials
520
20%
68
Magic 5-gon ring
21255
25%
66
Diophantine equation
20151
25%
77
Prime summations
19577
25%
83
Path sum: four ways
18509
25%
75
Singular integer right triangles
18399
25%
96
Su Doku
17496
25%
104
Pandigital Fibonacci ends
16429
25%
120
Square remainders
13966
25%
124
Ordered radicals
13870
25%
125
Palindromic sums
13679
25%
179
Consecutive positive divisors
11289
25%
187
Semiprimes
11223
25%
203
Squarefree Binomial Coefficients
9172
25%
348
Sum of a square and a cube
3012
25%
401
Sum of squares of divisors
2524
25%
512
Sums of totients of powers
1460
25%
425
Prime connection
1431
25%
479
Roots on the Rise
1263
25%
531
Chinese leftovers
1097
25%
571
Super Pandigital Numbers
1067
25%
675
2^{\omega(n)}
674
25%
752
Powers of 1+\sqrt 7
510
25%
78
Coin partitions
17255
30%
100
Arranged probability
16576
30%
95
Amicable chains
14576
30%
108
Diophantine reciprocals I
12802
30%
119
Digit power sum
12530
30%
123
Prime square remainders
11656
30%
173
Using up to one million tiles how many different "hollow" square laminae can be formed?
9119
30%
204
Generalised Hamming Numbers
7327
30%
293
Pseudo-Fortunate Numbers
2952
30%
451
Modular inverses
1394
30%
485
Maximum number of divisors
1127
30%
443
GCD sequence
1106
30%
435
Polynomials of Fibonacci numbers
1091
30%
581
47-smooth triangular numbers
819
30%
784
Reciprocal Pairs
284
30%
94
Almost equilateral triangles
12588
35%
93
Arithmetic expressions
12028
35%
98
Anagramic squares
11603
35%
243
Resilience
9549
35%
191
Prize Strings
7083
35%
188
The hyperexponentiation of a number
6391
35%
303
Multiples with small digits
3603
35%
277
A Modified Collatz sequence
3217
35%
349
Langton's ant
1900
35%
288
An enormous factorial
1633
35%
343
Fractional Sequences
1391
35%
463
A weird recurrence relation
1062
35%
417
Reciprocal cycles II
838
35%
565
Divisibility of sum of divisors
590
35%
625
Gcd sum
564
35%
621
Expressing an integer as the sum of triangular numbers
530
35%
545
Faulhaber's Formulas
510
35%
110
Diophantine reciprocals II
8167
40%
131
Prime cube partnership
7410
40%
174
Counting the number of "hollow" square laminae that can form one, two, three, ... distinct arrangements
5852
40%
231
The prime factorisation of binomial coefficients
5436
40%
214
Totient Chains
5194
40%
235
An Arithmetic Geometric sequence
4986
40%
207
Integer partition equations
4707
40%
304
Primonacci
2142
40%
365
A huge binomial coefficient
1229
40%
487
Sums of power sums
627
40%
634
Numbers of the form a^2b^3
573
40%
748
Upside down Diophantine equation
268
40%
111
Primes with runs
7303
45%
134
Prime pair connection
7048
45%
118
Pandigital prime sets
7018
45%
135
Same differences
6415
45%
132
Large repunit factors
6363
45%
129
Repunit divisibility
6319
45%
130
Composites with prime repunit property
5938
45%
138
Special isosceles triangles
5847
45%
142
Perfect Square Collection
5831
45%
197
Investigating the behaviour of a recursively defined sequence
4888
45%
183
Maximum product of parts
4661
45%
225
Tribonacci non-divisors
4443
45%
216
Investigating the primality of numbers of the form 2
n
2
-1
4058
45%
291
Panaitopol Primes
1420
45%
642
Sum of largest prime factors
335
45%
127
abc-hits
6265
50%
136
Singleton difference
5687
50%
133
Repunit nonfactors
5543
50%
137
Fibonacci golden nuggets
5539
50%
146
Investigating a Prime Pattern
5059
50%
169
Exploring the number of different ways a number can be expressed as a sum of powers of 2
5045
50%
211
Divisor Square Sum
4160
50%
320
Factorials divisible by a huge integer
849
50%
521
Smallest prime factor
715
50%
708
Twos are all you need
282
50%
140
Modified Fibonacci golden nuggets
4343
55%
193
Squarefree Numbers
3313
55%
678
Fermat-like Equations
221
55%
160
Factorial trailing digits
3486
60%
182
RSA encryption
2589
60%
271
Modular Cubes, part 1
2346
60%
196
Prime triplets
2555
65%
221
Alexandrian Integers
2052
65%
273
Sum of Squares
1360
70%
248
Numbers for which Euler’s totient function equals 13!
1283
70%
379
Least common multiple count
505
70%
192
Best Approximations
1583
75%
795
Alternating GCD Sum
195
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