ID

Title Solved by Difficulty
493Under The Rainbow527010%
692Siegbert and Jo114310%
710One Million Members97510%
725Digit sum numbers85210%
743Window into a Matrix83710%
788Dominating Numbers58610%
205Dice Game1499315%
301Nim642615%
504Square on the Inside300215%
709Even Stevens70115%
755Not Zeckendorf64515%
323Bitwise-OR operations on random integers386120%
315Digital root clocks337120%
587Concave triangle302820%
491Double pandigital number divisible by 11211320%
613Pythagorean Ant172620%
607Marsh Crossing164820%
518Prime triples and geometric sequences155720%
577Counting hexagons152220%
630Crossed lines93520%
679Freefarea76520%
713Turán's water heating system60620%
7063-Like Numbers48120%
731A Stoneham Number45020%
793Median of Products38520%
772Balanceable k-bounded partitions36920%
91Right triangles with integer coordinates1573425%
351Hexagonal orchards254625%
329Prime Frog248825%
336Maximix Arrangements204025%
358Cyclic numbers160225%
359Hilbert's New Hotel151825%
605Pairwise Coin-Tossing Game80925%
662Fibonacci paths72825%
714Duodigits61925%
6432-Friendly55825%
727Triangle of Circular Arcs43825%
759A squared recurrence relation43525%
722Slowly converging series43325%
739Summation of Summations42925%
712Exponent Difference42425%
717Summation of a Modular Formula41025%
776Digit Sum Division39725%
705Total Inversion Count of Divided Sequences39025%
733Ascending subsequences38925%
779Prime Factor and Exponent35325%
116Red, green or blue tiles1227130%
113Non-bouncy numbers1121030%
321Swapping Counters171330%
313Sliding game158630%
389Platonic Dice151730%
461Almost Pi116830%
371Licence plates116730%
340Crazy Function109530%
510Tangent Circles99230%
523First Sort I95730%
458Permutations of Project90330%
506Clock sequence85230%
628Open chess positions75230%
561Divisor Pairs73330%
527Randomized Binary Search70330%
555McCarthy 91 function67030%
543Prime-Sum Numbers66130%
612Friend numbers63930%
540Counting primitive Pythagorean triples61330%
624Two heads are better than one58930%
697Randomly Decaying Sequence50230%
657Incomplete words49230%
655Divisible Palindromes47530%
770Delphi Flip41330%
647Linear Transformations of Polygonal Numbers40930%
698123 Numbers39030%
649Low-Prime Chessboard Nim37330%
721High powers of irrational numbers36530%
724Drone Delivery34230%
737Coin Loops30930%
778Freshman's Product30330%
756Approximating a Sum28830%
86Cuboid route1296135%
84Monopoly odds1289335%
101Optimum polynomial1169135%
117Red, green, and blue tiles1125935%
107Minimal network1114235%
114Counting block combinations I1097935%
115Counting block combinations II1002435%
121Disc game prize fund981735%
297Zeckendorf Representation276635%
317Firecracker263435%
333Special partitions121335%
363Bézier Curves109635%
378Triangle Triples84335%
430Range flips83835%
539Odd elimination78935%
437Fibonacci primitive roots76435%
392Enmeshed unit circle76035%
457A polynomial modulo the square of a prime75935%
473Phigital number base71435%
595Incremental Random Sort59935%
537Counting tuples59435%
600Integer sided equiangular hexagons58835%
548Gozinta Chains58735%
575Wandering Robots56735%
615The millionth number with at least one million prime factors56135%
610Roman Numerals II55035%
593Fleeting Medians51935%
602Product of Head Counts47835%
641A Long Row of Dice45235%
632Square prime factors45035%
760Sum over Bitwise Operators35835%
663Sums of subarrays32935%
718Unreachable Numbers30535%
673Beds and Desks30435%
711Binary Blackboard29435%
734A bit of prime28235%
750Optimal Card Stacking27735%
720Unpredictable Permutations27435%
744What? Where? When?25735%
766Sliding Block Puzzle24435%
746A Messy Dinner23935%
738Counting Ordered Factorisations23735%
794Seventeen Points20735%
90Cube digit pairs1148240%
88Product-sum numbers1030140%
122Efficient exponentiation788640%
265Binary Circles419540%
307Chip Defects162640%
287Quadtree encoding (a simple compression algorithm)142140%
501Eight Divisors128840%
310Nim Square112140%
327Rooms of Doom112040%
449Chocolate covered candy88040%
375Minimum of subsequences86640%
469Empty chairs72440%
386Maximum length of an antichain71040%
455Powers With Trailing Digits69440%
395Pythagorean tree68140%
374Maximum Integer Partition Product66940%
418Factorisation triples66940%
366Stone Game III66240%
396Weak Goodstein sequence65140%
431Square Space Silo59840%
405A rectangular tiling59140%
498Remainder of polynomial division50240%
497Drunken Tower of Hanoi49840%
604Convex path in square48240%
616Creative numbers46740%
598Split Divisibilities46440%
515Dissonant Numbers44940%
552Chinese leftovers II41940%
588Quintinomial coefficients41540%
617Mirror Power Sequence36840%
638Weighted lattice paths35040%
753Fermat Equation34340%
635Subset sums32340%
538Maximum quadrilaterals30840%
670Colouring a Strip30840%
683The Chase II30240%
701Random connected area30140%
764Asymmetric Diophantine Equation29240%
660Pandigital Triangles28340%
693Finite Sequence Generator26940%
646Bounded Divisors25840%
691Long substring with many repetitions24740%
728Circle of Coins24440%
775Saving Paper20540%
732Standing on the shoulders of trolls19340%
787Bézout's Game15840%
109Darts824645%
103Special subset sums: optimum816045%
105Special subset sums: testing815745%
162Hexadecimal numbers536245%
164Numbers for which no three consecutive digits have a sum greater than a given value325645%
377Sum of digits - experience #1370045%
411Uphill paths62845%
341Golomb's self-describing sequence56945%
452Long Products56045%
480The Last Question55945%
399Squarefree Fibonacci Numbers55245%
509Divisor Nim54245%
368A Kempner-like series54045%
294Sum of digits - experience #2352845%
525Rolling Ellipse47745%
423Consecutive die throws46945%
517A real recursion44145%
476Circle Packing II40945%
603Substring sums of prime concatenations40445%
520Simbers38845%
619Square subsets38145%
569Prime Mountain Range37845%
654Neighbourly Constraints31945%
563Robot Welders31245%
637Flexible digit sum31045%
623Lambda Count30045%
669The King's Banquet29445%
653Frictionless Tube29145%
703Circular Logic II26945%
648Skipping Squares26745%
687Shuffling Cards26245%
666Polymorphic Bacteria26145%
790Clock Grid21345%
716Grid Graphs20745%
106Special subset sums: meta-testing648250%
144Investigating multiple reflections of a laser beam629650%
139Pythagorean tiles565250%
151Paper sheets of standard sizes: an expected-value problem552850%
148Exploring Pascal's triangle514450%
149Searching for a maximum-sum subsequence483550%
190Maximising a weighted product415250%
166Criss Cross409750%
215Crack-free Walls369950%
234Semidivisible numbers325350%
230Fibonacci Words288350%
286Scoring probabilities212750%
267Billionaire199550%
300Protein folding108550%
278Linear Combinations of Semiprimes103950%
3182011 nines92950%
312Cyclic paths on Sierpiński graphs83250%
309Integer Ladders80450%
393Migrating ants75550%
324Building a tower69350%
364Comfortable distance69050%
421Prime factors of n15+162850%
408Admissible paths through a grid55950%
290Digital Signature54150%
342The totient of a square is a cube50050%
412Gnomon numbering48250%
419Look and say sequence48150%
353Risky moon47650%
383Divisibility comparison between factorials46650%
454Diophantine reciprocals III46050%
551Sum of digits sequence45450%
475Music festival43550%
467Superinteger41750%
474Last digits of divisors39950%
406Guessing Game36950%
445Retractions A36850%
332Spherical triangles36750%
583Heron Envelopes36150%
606Gozinta Chains II36150%
596Number of lattice points in a hyperball34550%
519Tricoloured Coin Fountains33250%
360Scary Sphere33050%
640Shut the Box33050%
572Idempotent matrices32350%
533Minimum values of the Carmichael function31250%
582Nearly isosceles 120 degree triangles31050%
633Square prime factors II30450%
496Incenter and circumcenter of triangle29350%
672One more one26050%
574Verifying Primes25750%
6825-Smooth Pairs25450%
656Palindromic sequences22850%
676Matching Digit Sums22750%
681Maximal Area21350%
758Buckets of Water20750%
736Paths to Equality20050%
726Falling bottles17950%
762Amoebas in a 2D grid16750%
773Ruff Numbers16550%
783Urns16150%
789Minimal pairing modulo p14950%
128Hexagonal tile differences503755%
126Cuboid layers475255%
150Searching a triangular array for a sub-triangle having minimum-sum395055%
172Investigating numbers with few repeated digits377155%
158Exploring strings for which only one character comes lexicographically after its neighbour to the left362855%
178Step Numbers340055%
185Number Mind310955%
218Perfect right-angled triangles301955%
250250250297155%
220Heighway Dragon218355%
284Steady Squares124155%
285Pythagorean odds119755%
306Paper-strip Game117055%
281Pizza Toppings94855%
316Numbers in decimal expansions64555%
388Distinct Lines56555%
394Eating pie52055%
326Modulo Summations51755%
436Unfair wager44455%
409Nim Extreme44355%
511Sequences with nice divisibility properties39455%
352Blood tests39355%
456Triangles containing the origin II39255%
402Integer-valued polynomials39055%
367Bozo sort36755%
400Fibonacci tree game35455%
403Lattice points enclosed by parabola and line34855%
614Special partitions 229855%
532Nanobots on Geodesics29555%
534Weak Queens29055%
567Reciprocal games I28155%
557Cutting triangles27855%
568Reciprocal games II27055%
398Cutting rope26755%
570Snowflakes26555%
665Proportionate Nim23955%
658Incomplete words II23355%
576Irrational jumps22855%
629Scatterstone Nim22755%
661A Long Chess Match21355%
707Lights Out20755%
740Secret Santa18755%
785Symmetric Diophantine equation15855%
141Investigating progressive numbers, n, which are also square393360%
155Counting Capacitor Circuits359060%
159Digital root sums of factorisations328660%
186Connectedness of a network284460%
202Laserbeam252660%
249Prime Subset Sums252660%
209Circular Logic248760%
213Flea Circus230760%
240Top Dice216960%
222Sphere Packing208260%
308An amazing Prime-generating Automaton75960%
279Triangles with integral sides and an integral angle 71860%
298Selective Amnesia65560%
299Three similar triangles61860%
305Reflexive Position59260%
356Largest roots of cubic polynomials58160%
296Angular Bisector and Tangent56960%
390Triangles with non rational sides and integral area55960%
369Badugi45960%
302Strong Achilles Numbers42760%
530GCD of Divisors42760%
4202x2 positive integer matrix42560%
424Kakuro39260%
442Eleven-free integers38260%
440GCD and Tiling36360%
446Retractions B35160%
492Exploding sequence33860%
550Divisor game33060%
380Amazing Mazes!32760%
382Generating polygons32560%
460An ant on the move32360%
350Constraining the least greatest and the greatest least32260%
404Crisscross Ellipses32060%
611Hallway of square steps31860%
462Permutation of 3-smooth numbers31060%
464Möbius function and intervals30460%
503Compromise or persist30160%
444The Roundtable Lottery29960%
513Integral median29760%
526Largest prime factors of consecutive numbers29060%
599Distinct Colourings of a Rubik's Cube28960%
535Fractal Sequence27960%
536Modulo power identity 27860%
414Kaprekar constant27560%
592Factorial trailing digits 227260%
528Constrained Sums26260%
472Comfortable Distance II25760%
590Sets with a given Least Common Multiple24960%
372Pencils of rays24360%
627Counting products23060%
564Maximal polygons22460%
689Binary Series21560%
690Tom and Jerry18460%
747Triangular Pizza17860%
715Sextuplet Norms17460%
767Window into a Matrix II15260%
791Average and Variance13260%
147Rectangles in cross-hatched grids301865%
171Finding numbers for which the sum of the squares of the digits is a square276865%
143Investigating the Torricelli point of a triangle274465%
157Solving the diophantine equation 1/a+1/b= p/10n 270865%
152Writing 1/2 as a sum of inverse squares268065%
168Number Rotations264265%
154Exploring Pascal's pyramid263565%
153Investigating Gaussian Integers261065%
165Intersections257865%
200Find the 200th prime-proof sqube containing the contiguous sub-string "200"235065%
201Subsets with a unique sum229065%
227The Chase209065%
239Twenty-two Foolish Primes182565%
232The Race175465%
226A Scoop of Blancmange172465%
247Squares under a hyperbola145665%
266Pseudo Square Root96765%
274Divisibility Multipliers69365%
280Ant and seeds57565%
292Pythagorean Polygons56565%
370Geometric triangles51265%
335Gathering the beans50365%
334Spilling the beans47065%
433Steps in Euclid's algorithm46465%
354Distances in a bee's honeycomb 42965%
441The inverse summation of coprime couples34765%
384Rudin-Shapiro sequence32565%
466Distinct terms in a multiplication table30865%
477Number Sequence Game25165%
558Irrational base23965%
470Super Ramvok22365%
542Geometric Progression with Maximum Sum21765%
735Divisors of 2n^219365%
631Constrained Permutations19165%
685Inverse Digit Sum II19065%
680Yarra Gnisrever18065%
664An infinite game17865%
765Trillionaire17265%
723Pythagorean Quadrilaterals16965%
730Shifted Pythagorean Triples16365%
729Range of periodic sequence15165%
782Distinct Rows and Columns12965%
156Counting Digits241670%
233Lattice points on a circle229570%
161Triominoes210770%
189Tri-colouring a triangular grid203270%
170Find the largest 0 to 9 pandigital that can be formed by concatenating products197770%
181Investigating in how many ways objects of two different colours can be grouped195870%
176Right-angled triangles that share a cathetus188070%
163Cross-hatched triangles179170%
208Robot Walks174170%
210Obtuse Angled Triangles168770%
258A lagged Fibonacci sequence158470%
237Tours on a 4 x n playing board155370%
223Almost right-angled triangles I150370%
217Balanced Numbers149170%
259Reachable Numbers147370%
219Skew-cost coding146170%
229Four Representations using Squares145870%
268Counting numbers with at least four distinct prime factors less than 100142970%
212Combined Volume of Cuboids136070%
228Minkowski Sums131070%
244Sliders130070%
199Iterative Circle Packing115970%
282The Ackermann function98270%
175Fractions involving the number of different ways a number can be expressed as a sum of powers of 297870%
251Cardano Triplets77870%
260Stone Game68770%
339Peredur fab Efrawg53870%
355Maximal coprime subset52170%
330Euler's Number51670%
337Totient Stairstep Sequences50470%
432Totient sum47470%
362Squarefree factors46570%
322Binomial coefficients divisible by 1044970%
311Biclinic Integral Quadrilaterals42470%
385Ellipses inside triangles27670%
410Circle and tangent line27370%
376Nontransitive sets of dice26570%
397Triangle on parabola26370%
468Smooth divisors of binomial coefficients26270%
486Palindrome-containing strings24870%
639Summing a multiplicative function24270%
481Chef Showdown23570%
626Counting Binary Matrices21370%
547Distance of random points within hollow square laminae21070%
695Random Rectangles19170%
652Distinct values of a proto-logarithmic function16270%
651Patterned Cylinders15870%
167Investigating Ulam sequences166975%
184Triangles containing the origin162175%
180Rational zeros of a function of three variables155775%
194Coloured Configurations138075%
195Inscribed circles of triangles with one angle of 60 degrees137975%
276Primitive Triangles107175%
242Odd Triplets103975%
263An engineers' dream come true101675%
253Tidying up100875%
238Infinite string tour95175%
254Sums of Digit Factorials95075%
255Rounded Square Roots84875%
224Almost right-angled triangles II68475%
283Integer sided triangles for which the area/perimeter ratio is integral62975%
413One-child Numbers37275%
434Rigid graphs33475%
373Circumscribed Circles33275%
560Coprime Nim29875%
391Hopping Game27175%
422Sequence of points on a hyperbola26375%
426Box-ball system25175%
580Squarefree Hilbert numbers23575%
586Binary Quadratic Form22575%
524First Sort II21575%
471Triangle inscribed in ellipse21375%
295Lenticular holes21075%
645Every Day is a Holiday19875%
562Maximal perimeter18275%
674Solving \mathcal{I}-equations16775%
742Minimum area of a convex grid polygon15475%
177Integer angled Quadrilaterals126480%
198Ambiguous Numbers110580%
272Modular Cubes, part 295480%
241Perfection Quotients92280%
252Convex Holes82180%
245Coresilience80780%
246Tangents to an ellipse79680%
256Tatami-Free Rooms72580%
269Polynomials with at least one integer root68080%
270Cutting Squares63380%
325Stone Game II58980%
314The Mouse on the Moon49980%
236Luxury Hampers45880%
262Mountain Range34780%
448Average least common multiple32780%
608Divisor Sums29080%
416A frog's trip28880%
488Unbalanced Nim23280%
554Centaurs on a chess board22480%
578Integers with decreasing prime powers21880%
573Unfair race19780%
667Moving Pentagon19280%
699Triffle Numbers17780%
620Planetary Gears16980%
671Colouring a Loop15780%
741Binary grid colouring14480%
771Pseudo Geometric Sequences10380%
777Lissajous Curves9080%
261Pivotal Square Sums67985%
257Angular Bisectors67785%
275Balanced Sculptures58885%
264Triangle Centres55085%
522Hilbert's Blackout25985%
52910-substrings23985%
556Squarefree Gaussian Integers23785%
546The Floor's Revenge22385%
465Polar polygons20985%
482The incenter of a triangle20485%
553Power sets of power sets20285%
594Rhombus Tilings17785%
289Eulerian Cycles48290%
319Bounded Sequences39490%
361Subsequence of Thue-Morse sequence29790%
544Chromatic Conundrum23490%
428Necklace of circles23390%
508Integers in base i-122990%
507Shortest Lattice Vector20890%
514Geoboard Shapes20490%
505Bidirectional Recurrence20290%
541Divisibility of Harmonic Number Denominators19890%
636Restricted Factorisations17990%
677Coloured Graphs16990%
644Squares on the line15190%
761Runner and Swimmer12590%
769Binary Quadratic Form II10890%
768Chandelier9890%
774Conjunctive Sequences9890%
781Feynman Diagrams9390%
786Billiard8490%
792Too Many Twos7190%
328Lowest-cost Search41595%
338Cutting Rectangular Grid Paper32495%
427n-sequences30195%
447Retractions C28495%
490Jumping frog28495%
438Integer part of polynomial equation's solutions26795%
453Lattice Quadrilaterals21195%
589Poohsticks Marathon19495%
591Best Approximations by Quadratic Integers18495%
702Jumping Flea14795%
331Cross flips394100%
439Sum of sum of divisors380100%
484Arithmetic Derivative335100%
499St. Petersburg Lottery314100%
344Silver dollar game308100%
415Titanic sets299100%
502Counting Castles283100%
495Writing n as the product of k distinct positive integers277100%
459Flipping game227100%
489Common factors between two sequences223100%
483Repeated permutation217100%
494Collatz prefix families205100%
584Birthday Problem Revisited195100%
450Hypocycloid and Lattice points189100%
478Mixtures182100%
559Permuted Matrices181100%
585Nested square roots167100%
597Torpids162100%
696Mahjong162100%
579Lattice points in lattice cubes158100%
566Cake Icing Puzzle153100%
763Amoebas in a 3D grid55100%
780Toriangulations47100%
800Hybrid Integers542-
804Counting Binary Quadratic Representations221-
799Pentagonal Puzzle147-
796A Grand Shuffle138-
802Iterated Composition135-
801x^y \equiv y^x130-
797Cyclogenic Polynomials125-
803Pseudorandom sequence117-
798Card Stacking Game60-