ID
Title
Solved by
Difficulty
493
Under The Rainbow
5270
10%
692
Siegbert and Jo
1143
10%
710
One Million Members
975
10%
725
Digit sum numbers
852
10%
743
Window into a Matrix
837
10%
788
Dominating Numbers
586
10%
205
Dice Game
14993
15%
301
Nim
6426
15%
504
Square on the Inside
3002
15%
709
Even Stevens
701
15%
755
Not Zeckendorf
645
15%
323
Bitwise-OR operations on random integers
3861
20%
315
Digital root clocks
3371
20%
587
Concave triangle
3028
20%
491
Double pandigital number divisible by 11
2113
20%
613
Pythagorean Ant
1726
20%
607
Marsh Crossing
1648
20%
518
Prime triples and geometric sequences
1557
20%
577
Counting hexagons
1522
20%
630
Crossed lines
935
20%
679
Freefarea
765
20%
713
Turán's water heating system
606
20%
706
3-Like Numbers
481
20%
731
A Stoneham Number
450
20%
793
Median of Products
385
20%
772
Balanceable k-bounded partitions
369
20%
91
Right triangles with integer coordinates
15734
25%
351
Hexagonal orchards
2546
25%
329
Prime Frog
2488
25%
336
Maximix Arrangements
2040
25%
358
Cyclic numbers
1602
25%
359
Hilbert's New Hotel
1518
25%
605
Pairwise Coin-Tossing Game
809
25%
662
Fibonacci paths
728
25%
714
Duodigits
619
25%
643
2-Friendly
558
25%
727
Triangle of Circular Arcs
438
25%
759
A squared recurrence relation
435
25%
722
Slowly converging series
433
25%
739
Summation of Summations
429
25%
712
Exponent Difference
424
25%
717
Summation of a Modular Formula
410
25%
776
Digit Sum Division
397
25%
705
Total Inversion Count of Divided Sequences
390
25%
733
Ascending subsequences
389
25%
779
Prime Factor and Exponent
353
25%
116
Red, green or blue tiles
12271
30%
113
Non-bouncy numbers
11210
30%
321
Swapping Counters
1713
30%
313
Sliding game
1586
30%
389
Platonic Dice
1517
30%
461
Almost Pi
1168
30%
371
Licence plates
1167
30%
340
Crazy Function
1095
30%
510
Tangent Circles
992
30%
523
First Sort I
957
30%
458
Permutations of Project
903
30%
506
Clock sequence
852
30%
628
Open chess positions
752
30%
561
Divisor Pairs
733
30%
527
Randomized Binary Search
703
30%
555
McCarthy 91 function
670
30%
543
Prime-Sum Numbers
661
30%
612
Friend numbers
639
30%
540
Counting primitive Pythagorean triples
613
30%
624
Two heads are better than one
589
30%
697
Randomly Decaying Sequence
502
30%
657
Incomplete words
492
30%
655
Divisible Palindromes
475
30%
770
Delphi Flip
413
30%
647
Linear Transformations of Polygonal Numbers
409
30%
698
123 Numbers
390
30%
649
Low-Prime Chessboard Nim
373
30%
721
High powers of irrational numbers
365
30%
724
Drone Delivery
342
30%
737
Coin Loops
309
30%
778
Freshman's Product
303
30%
756
Approximating a Sum
288
30%
86
Cuboid route
12961
35%
84
Monopoly odds
12893
35%
101
Optimum polynomial
11691
35%
117
Red, green, and blue tiles
11259
35%
107
Minimal network
11142
35%
114
Counting block combinations I
10979
35%
115
Counting block combinations II
10024
35%
121
Disc game prize fund
9817
35%
297
Zeckendorf Representation
2766
35%
317
Firecracker
2634
35%
333
Special partitions
1213
35%
363
Bézier Curves
1096
35%
378
Triangle Triples
843
35%
430
Range flips
838
35%
539
Odd elimination
789
35%
437
Fibonacci primitive roots
764
35%
392
Enmeshed unit circle
760
35%
457
A polynomial modulo the square of a prime
759
35%
473
Phigital number base
714
35%
595
Incremental Random Sort
599
35%
537
Counting tuples
594
35%
600
Integer sided equiangular hexagons
588
35%
548
Gozinta Chains
587
35%
575
Wandering Robots
567
35%
615
The millionth number with at least one million prime factors
561
35%
610
Roman Numerals II
550
35%
593
Fleeting Medians
519
35%
602
Product of Head Counts
478
35%
641
A Long Row of Dice
452
35%
632
Square prime factors
450
35%
760
Sum over Bitwise Operators
358
35%
663
Sums of subarrays
329
35%
718
Unreachable Numbers
305
35%
673
Beds and Desks
304
35%
711
Binary Blackboard
294
35%
734
A bit of prime
282
35%
750
Optimal Card Stacking
277
35%
720
Unpredictable Permutations
274
35%
744
What? Where? When?
257
35%
766
Sliding Block Puzzle
244
35%
746
A Messy Dinner
239
35%
738
Counting Ordered Factorisations
237
35%
794
Seventeen Points
207
35%
90
Cube digit pairs
11482
40%
88
Product-sum numbers
10301
40%
122
Efficient exponentiation
7886
40%
265
Binary Circles
4195
40%
307
Chip Defects
1626
40%
287
Quadtree encoding (a simple compression algorithm)
1421
40%
501
Eight Divisors
1288
40%
310
Nim Square
1121
40%
327
Rooms of Doom
1120
40%
449
Chocolate covered candy
880
40%
375
Minimum of subsequences
866
40%
469
Empty chairs
724
40%
386
Maximum length of an antichain
710
40%
455
Powers With Trailing Digits
694
40%
395
Pythagorean tree
681
40%
374
Maximum Integer Partition Product
669
40%
418
Factorisation triples
669
40%
366
Stone Game III
662
40%
396
Weak Goodstein sequence
651
40%
431
Square Space Silo
598
40%
405
A rectangular tiling
591
40%
498
Remainder of polynomial division
502
40%
497
Drunken Tower of Hanoi
498
40%
604
Convex path in square
482
40%
616
Creative numbers
467
40%
598
Split Divisibilities
464
40%
515
Dissonant Numbers
449
40%
552
Chinese leftovers II
419
40%
588
Quintinomial coefficients
415
40%
617
Mirror Power Sequence
368
40%
638
Weighted lattice paths
350
40%
753
Fermat Equation
343
40%
635
Subset sums
323
40%
538
Maximum quadrilaterals
308
40%
670
Colouring a Strip
308
40%
683
The Chase II
302
40%
701
Random connected area
301
40%
764
Asymmetric Diophantine Equation
292
40%
660
Pandigital Triangles
283
40%
693
Finite Sequence Generator
269
40%
646
Bounded Divisors
258
40%
691
Long substring with many repetitions
247
40%
728
Circle of Coins
244
40%
775
Saving Paper
205
40%
732
Standing on the shoulders of trolls
193
40%
787
Bézout's Game
158
40%
109
Darts
8246
45%
103
Special subset sums: optimum
8160
45%
105
Special subset sums: testing
8157
45%
162
Hexadecimal numbers
5362
45%
164
Numbers for which no three consecutive digits have a sum greater than a given value
3256
45%
377
Sum of digits - experience #13
700
45%
411
Uphill paths
628
45%
341
Golomb's self-describing sequence
569
45%
452
Long Products
560
45%
480
The Last Question
559
45%
399
Squarefree Fibonacci Numbers
552
45%
509
Divisor Nim
542
45%
368
A Kempner-like series
540
45%
294
Sum of digits - experience #23
528
45%
525
Rolling Ellipse
477
45%
423
Consecutive die throws
469
45%
517
A real recursion
441
45%
476
Circle Packing II
409
45%
603
Substring sums of prime concatenations
404
45%
520
Simbers
388
45%
619
Square subsets
381
45%
569
Prime Mountain Range
378
45%
654
Neighbourly Constraints
319
45%
563
Robot Welders
312
45%
637
Flexible digit sum
310
45%
623
Lambda Count
300
45%
669
The King's Banquet
294
45%
653
Frictionless Tube
291
45%
703
Circular Logic II
269
45%
648
Skipping Squares
267
45%
687
Shuffling Cards
262
45%
666
Polymorphic Bacteria
261
45%
790
Clock Grid
213
45%
716
Grid Graphs
207
45%
106
Special subset sums: meta-testing
6482
50%
144
Investigating multiple reflections of a laser beam
6296
50%
139
Pythagorean tiles
5652
50%
151
Paper sheets of standard sizes: an expected-value problem
5528
50%
148
Exploring Pascal's triangle
5144
50%
149
Searching for a maximum-sum subsequence
4835
50%
190
Maximising a weighted product
4152
50%
166
Criss Cross
4097
50%
215
Crack-free Walls
3699
50%
234
Semidivisible numbers
3253
50%
230
Fibonacci Words
2883
50%
286
Scoring probabilities
2127
50%
267
Billionaire
1995
50%
300
Protein folding
1085
50%
278
Linear Combinations of Semiprimes
1039
50%
318
2011 nines
929
50%
312
Cyclic paths on Sierpiński graphs
832
50%
309
Integer Ladders
804
50%
393
Migrating ants
755
50%
324
Building a tower
693
50%
364
Comfortable distance
690
50%
421
Prime factors of
n
15
+1
628
50%
408
Admissible paths through a grid
559
50%
290
Digital Signature
541
50%
342
The totient of a square is a cube
500
50%
412
Gnomon numbering
482
50%
419
Look and say sequence
481
50%
353
Risky moon
476
50%
383
Divisibility comparison between factorials
466
50%
454
Diophantine reciprocals III
460
50%
551
Sum of digits sequence
454
50%
475
Music festival
435
50%
467
Superinteger
417
50%
474
Last digits of divisors
399
50%
406
Guessing Game
369
50%
445
Retractions A
368
50%
332
Spherical triangles
367
50%
583
Heron Envelopes
361
50%
606
Gozinta Chains II
361
50%
596
Number of lattice points in a hyperball
345
50%
519
Tricoloured Coin Fountains
332
50%
360
Scary Sphere
330
50%
640
Shut the Box
330
50%
572
Idempotent matrices
323
50%
533
Minimum values of the Carmichael function
312
50%
582
Nearly isosceles 120 degree triangles
310
50%
633
Square prime factors II
304
50%
496
Incenter and circumcenter of triangle
293
50%
672
One more one
260
50%
574
Verifying Primes
257
50%
682
5-Smooth Pairs
254
50%
656
Palindromic sequences
228
50%
676
Matching Digit Sums
227
50%
681
Maximal Area
213
50%
758
Buckets of Water
207
50%
736
Paths to Equality
200
50%
726
Falling bottles
179
50%
762
Amoebas in a 2D grid
167
50%
773
Ruff Numbers
165
50%
783
Urns
161
50%
789
Minimal pairing modulo p
149
50%
128
Hexagonal tile differences
5037
55%
126
Cuboid layers
4752
55%
150
Searching a triangular array for a sub-triangle having minimum-sum
3950
55%
172
Investigating numbers with few repeated digits
3771
55%
158
Exploring strings for which only one character comes lexicographically after its neighbour to the left
3628
55%
178
Step Numbers
3400
55%
185
Number Mind
3109
55%
218
Perfect right-angled triangles
3019
55%
250
250250
2971
55%
220
Heighway Dragon
2183
55%
284
Steady Squares
1241
55%
285
Pythagorean odds
1197
55%
306
Paper-strip Game
1170
55%
281
Pizza Toppings
948
55%
316
Numbers in decimal expansions
645
55%
388
Distinct Lines
565
55%
394
Eating pie
520
55%
326
Modulo Summations
517
55%
436
Unfair wager
444
55%
409
Nim Extreme
443
55%
511
Sequences with nice divisibility properties
394
55%
352
Blood tests
393
55%
456
Triangles containing the origin II
392
55%
402
Integer-valued polynomials
390
55%
367
Bozo sort
367
55%
400
Fibonacci tree game
354
55%
403
Lattice points enclosed by parabola and line
348
55%
614
Special partitions 2
298
55%
532
Nanobots on Geodesics
295
55%
534
Weak Queens
290
55%
567
Reciprocal games I
281
55%
557
Cutting triangles
278
55%
568
Reciprocal games II
270
55%
398
Cutting rope
267
55%
570
Snowflakes
265
55%
665
Proportionate Nim
239
55%
658
Incomplete words II
233
55%
576
Irrational jumps
228
55%
629
Scatterstone Nim
227
55%
661
A Long Chess Match
213
55%
707
Lights Out
207
55%
740
Secret Santa
187
55%
785
Symmetric Diophantine equation
158
55%
141
Investigating progressive numbers,
n
, which are also square
3933
60%
155
Counting Capacitor Circuits
3590
60%
159
Digital root sums of factorisations
3286
60%
186
Connectedness of a network
2844
60%
202
Laserbeam
2526
60%
249
Prime Subset Sums
2526
60%
209
Circular Logic
2487
60%
213
Flea Circus
2307
60%
240
Top Dice
2169
60%
222
Sphere Packing
2082
60%
308
An amazing Prime-generating Automaton
759
60%
279
Triangles with integral sides and an integral angle
718
60%
298
Selective Amnesia
655
60%
299
Three similar triangles
618
60%
305
Reflexive Position
592
60%
356
Largest roots of cubic polynomials
581
60%
296
Angular Bisector and Tangent
569
60%
390
Triangles with non rational sides and integral area
559
60%
369
Badugi
459
60%
302
Strong Achilles Numbers
427
60%
530
GCD of Divisors
427
60%
420
2x2 positive integer matrix
425
60%
424
Kakuro
392
60%
442
Eleven-free integers
382
60%
440
GCD and Tiling
363
60%
446
Retractions B
351
60%
492
Exploding sequence
338
60%
550
Divisor game
330
60%
380
Amazing Mazes!
327
60%
382
Generating polygons
325
60%
460
An ant on the move
323
60%
350
Constraining the least greatest and the greatest least
322
60%
404
Crisscross Ellipses
320
60%
611
Hallway of square steps
318
60%
462
Permutation of 3-smooth numbers
310
60%
464
Möbius function and intervals
304
60%
503
Compromise or persist
301
60%
444
The Roundtable Lottery
299
60%
513
Integral median
297
60%
526
Largest prime factors of consecutive numbers
290
60%
599
Distinct Colourings of a Rubik's Cube
289
60%
535
Fractal Sequence
279
60%
536
Modulo power identity
278
60%
414
Kaprekar constant
275
60%
592
Factorial trailing digits 2
272
60%
528
Constrained Sums
262
60%
472
Comfortable Distance II
257
60%
590
Sets with a given Least Common Multiple
249
60%
372
Pencils of rays
243
60%
627
Counting products
230
60%
564
Maximal polygons
224
60%
689
Binary Series
215
60%
690
Tom and Jerry
184
60%
747
Triangular Pizza
178
60%
715
Sextuplet Norms
174
60%
767
Window into a Matrix II
152
60%
791
Average and Variance
132
60%
147
Rectangles in cross-hatched grids
3018
65%
171
Finding numbers for which the sum of the squares of the digits is a square
2768
65%
143
Investigating the Torricelli point of a triangle
2744
65%
157
Solving the diophantine equation
1
/
a
+
1
/
b
=
p
/
10
n
2708
65%
152
Writing 1/2 as a sum of inverse squares
2680
65%
168
Number Rotations
2642
65%
154
Exploring Pascal's pyramid
2635
65%
153
Investigating Gaussian Integers
2610
65%
165
Intersections
2578
65%
200
Find the 200th prime-proof sqube containing the contiguous sub-string "200"
2350
65%
201
Subsets with a unique sum
2290
65%
227
The Chase
2090
65%
239
Twenty-two Foolish Primes
1825
65%
232
The Race
1754
65%
226
A Scoop of Blancmange
1724
65%
247
Squares under a hyperbola
1456
65%
266
Pseudo Square Root
967
65%
274
Divisibility Multipliers
693
65%
280
Ant and seeds
575
65%
292
Pythagorean Polygons
565
65%
370
Geometric triangles
512
65%
335
Gathering the beans
503
65%
334
Spilling the beans
470
65%
433
Steps in Euclid's algorithm
464
65%
354
Distances in a bee's honeycomb
429
65%
441
The inverse summation of coprime couples
347
65%
384
Rudin-Shapiro sequence
325
65%
466
Distinct terms in a multiplication table
308
65%
477
Number Sequence Game
251
65%
558
Irrational base
239
65%
470
Super Ramvok
223
65%
542
Geometric Progression with Maximum Sum
217
65%
735
Divisors of 2n^2
193
65%
631
Constrained Permutations
191
65%
685
Inverse Digit Sum II
190
65%
680
Yarra Gnisrever
180
65%
664
An infinite game
178
65%
765
Trillionaire
172
65%
723
Pythagorean Quadrilaterals
169
65%
730
Shifted Pythagorean Triples
163
65%
729
Range of periodic sequence
151
65%
782
Distinct Rows and Columns
129
65%
156
Counting Digits
2416
70%
233
Lattice points on a circle
2295
70%
161
Triominoes
2107
70%
189
Tri-colouring a triangular grid
2032
70%
170
Find the largest 0 to 9 pandigital that can be formed by concatenating products
1977
70%
181
Investigating in how many ways objects of two different colours can be grouped
1958
70%
176
Right-angled triangles that share a cathetus
1880
70%
163
Cross-hatched triangles
1791
70%
208
Robot Walks
1741
70%
210
Obtuse Angled Triangles
1687
70%
258
A lagged Fibonacci sequence
1584
70%
237
Tours on a 4 x n playing board
1553
70%
223
Almost right-angled triangles I
1503
70%
217
Balanced Numbers
1491
70%
259
Reachable Numbers
1473
70%
219
Skew-cost coding
1461
70%
229
Four Representations using Squares
1458
70%
268
Counting numbers with at least four distinct prime factors less than 100
1429
70%
212
Combined Volume of Cuboids
1360
70%
228
Minkowski Sums
1310
70%
244
Sliders
1300
70%
199
Iterative Circle Packing
1159
70%
282
The Ackermann function
982
70%
175
Fractions involving the number of different ways a number can be expressed as a sum of powers of 2
978
70%
251
Cardano Triplets
778
70%
260
Stone Game
687
70%
339
Peredur fab Efrawg
538
70%
355
Maximal coprime subset
521
70%
330
Euler's Number
516
70%
337
Totient Stairstep Sequences
504
70%
432
Totient sum
474
70%
362
Squarefree factors
465
70%
322
Binomial coefficients divisible by 10
449
70%
311
Biclinic Integral Quadrilaterals
424
70%
385
Ellipses inside triangles
276
70%
410
Circle and tangent line
273
70%
376
Nontransitive sets of dice
265
70%
397
Triangle on parabola
263
70%
468
Smooth divisors of binomial coefficients
262
70%
486
Palindrome-containing strings
248
70%
639
Summing a multiplicative function
242
70%
481
Chef Showdown
235
70%
626
Counting Binary Matrices
213
70%
547
Distance of random points within hollow square laminae
210
70%
695
Random Rectangles
191
70%
652
Distinct values of a proto-logarithmic function
162
70%
651
Patterned Cylinders
158
70%
167
Investigating Ulam sequences
1669
75%
184
Triangles containing the origin
1621
75%
180
Rational zeros of a function of three variables
1557
75%
194
Coloured Configurations
1380
75%
195
Inscribed circles of triangles with one angle of 60 degrees
1379
75%
276
Primitive Triangles
1071
75%
242
Odd Triplets
1039
75%
263
An engineers' dream come true
1016
75%
253
Tidying up
1008
75%
238
Infinite string tour
951
75%
254
Sums of Digit Factorials
950
75%
255
Rounded Square Roots
848
75%
224
Almost right-angled triangles II
684
75%
283
Integer sided triangles for which the area/perimeter ratio is integral
629
75%
413
One-child Numbers
372
75%
434
Rigid graphs
334
75%
373
Circumscribed Circles
332
75%
560
Coprime Nim
298
75%
391
Hopping Game
271
75%
422
Sequence of points on a hyperbola
263
75%
426
Box-ball system
251
75%
580
Squarefree Hilbert numbers
235
75%
586
Binary Quadratic Form
225
75%
524
First Sort II
215
75%
471
Triangle inscribed in ellipse
213
75%
295
Lenticular holes
210
75%
645
Every Day is a Holiday
198
75%
562
Maximal perimeter
182
75%
674
Solving \mathcal{I}-equations
167
75%
742
Minimum area of a convex grid polygon
154
75%
177
Integer angled Quadrilaterals
1264
80%
198
Ambiguous Numbers
1105
80%
272
Modular Cubes, part 2
954
80%
241
Perfection Quotients
922
80%
252
Convex Holes
821
80%
245
Coresilience
807
80%
246
Tangents to an ellipse
796
80%
256
Tatami-Free Rooms
725
80%
269
Polynomials with at least one integer root
680
80%
270
Cutting Squares
633
80%
325
Stone Game II
589
80%
314
The Mouse on the Moon
499
80%
236
Luxury Hampers
458
80%
262
Mountain Range
347
80%
448
Average least common multiple
327
80%
608
Divisor Sums
290
80%
416
A frog's trip
288
80%
488
Unbalanced Nim
232
80%
554
Centaurs on a chess board
224
80%
578
Integers with decreasing prime powers
218
80%
573
Unfair race
197
80%
667
Moving Pentagon
192
80%
699
Triffle Numbers
177
80%
620
Planetary Gears
169
80%
671
Colouring a Loop
157
80%
741
Binary grid colouring
144
80%
771
Pseudo Geometric Sequences
103
80%
777
Lissajous Curves
90
80%
261
Pivotal Square Sums
679
85%
257
Angular Bisectors
677
85%
275
Balanced Sculptures
588
85%
264
Triangle Centres
550
85%
522
Hilbert's Blackout
259
85%
529
10-substrings
239
85%
556
Squarefree Gaussian Integers
237
85%
546
The Floor's Revenge
223
85%
465
Polar polygons
209
85%
482
The incenter of a triangle
204
85%
553
Power sets of power sets
202
85%
594
Rhombus Tilings
177
85%
289
Eulerian Cycles
482
90%
319
Bounded Sequences
394
90%
361
Subsequence of Thue-Morse sequence
297
90%
544
Chromatic Conundrum
234
90%
428
Necklace of circles
233
90%
508
Integers in base i-1
229
90%
507
Shortest Lattice Vector
208
90%
514
Geoboard Shapes
204
90%
505
Bidirectional Recurrence
202
90%
541
Divisibility of Harmonic Number Denominators
198
90%
636
Restricted Factorisations
179
90%
677
Coloured Graphs
169
90%
644
Squares on the line
151
90%
761
Runner and Swimmer
125
90%
769
Binary Quadratic Form II
108
90%
768
Chandelier
98
90%
774
Conjunctive Sequences
98
90%
781
Feynman Diagrams
93
90%
786
Billiard
84
90%
792
Too Many Twos
71
90%
328
Lowest-cost Search
415
95%
338
Cutting Rectangular Grid Paper
324
95%
427
n-sequences
301
95%
447
Retractions C
284
95%
490
Jumping frog
284
95%
438
Integer part of polynomial equation's solutions
267
95%
453
Lattice Quadrilaterals
211
95%
589
Poohsticks Marathon
194
95%
591
Best Approximations by Quadratic Integers
184
95%
702
Jumping Flea
147
95%
331
Cross flips
394
100%
439
Sum of sum of divisors
380
100%
484
Arithmetic Derivative
335
100%
499
St. Petersburg Lottery
314
100%
344
Silver dollar game
308
100%
415
Titanic sets
299
100%
502
Counting Castles
283
100%
495
Writing n as the product of k distinct positive integers
277
100%
459
Flipping game
227
100%
489
Common factors between two sequences
223
100%
483
Repeated permutation
217
100%
494
Collatz prefix families
205
100%
584
Birthday Problem Revisited
195
100%
450
Hypocycloid and Lattice points
189
100%
478
Mixtures
182
100%
559
Permuted Matrices
181
100%
585
Nested square roots
167
100%
597
Torpids
162
100%
696
Mahjong
162
100%
579
Lattice points in lattice cubes
158
100%
566
Cake Icing Puzzle
153
100%
763
Amoebas in a 3D grid
55
100%
780
Toriangulations
47
100%
800
Hybrid Integers
542
-
804
Counting Binary Quadratic Representations
221
-
799
Pentagonal Puzzle
147
-
796
A Grand Shuffle
138
-
802
Iterated Composition
135
-
801
x^y \equiv y^x
130
-
797
Cyclogenic Polynomials
125
-
803
Pseudorandom sequence
117
-
798
Card Stacking Game
60
-