python3, gcc 5.2 c++14
| Problem | File | Result |
|---|---|---|
| Problem 1: Multiples of 3 and 5 | 1_multiples_of_3_and_5.py | 233168 |
| Problem 2: Even Fibonacci numbers | 2_even_fibonacci_number.py | 4613732 |
| Problem 3: Largest prime factor | 3_largest_prime_factor.py | 6857 |
| Problem 4: Largest palindrome product | 4_largest_palindrome_product.py | 906609 |
| Problem 5: Smallest multiple | 5_smallest_multiple.py | 232792560 |
| Problem 6: Sum square difference | 6_sum_square_difference.py | 25164150 |
| Problem 7: 10001st prime | 7_10001st_prime.py | 104743 |
| Problem 8: Largest product in a series | 8_largest_product_in_a_series.py | 23514624000 |
| Problem 9: Special Pythagorean triplet | 9_special_pythagorean_triplet.py | 31875000 |
| Problem 10: Summation of primes | 10_summation_of_primes.py | 142913828922 |
| Problem 11: Largest product in a grid | 11_largest_product_in_a_grid.py | 70600674 |
| Problem 12: Highly divisible triangular number | 12_highly_divisible_triangular_number.py | 76576500 |
| Problem 13: Large sum | 13_large_sum.py | 5537376230 |
| Problem 14: Longest Collatz sequence | 14_longest_collatz_sequence.py | 837799 |
| Problem 15: Lattice paths | 15_lattice_path.py | 137846528820 |
| Problem 16: Power digit sum | 16_power_digit_sum.py | 1366 |
| Problem 17: Number letter counts | 17_number_letter_counts.py | 21124 |
| Problem 18: Maximum path sum I | 18_maximum_path_sum_i.py | 1074 |
| Problem 19: Counting Sundays | 19_counting_sundays.py | 171 |
| Problem 20: Factorial digit sum | 20_factorial_digit_sum.py | 648 |
| Problem 21: Amicable numbers | 21_amicable_numbers.py | 31626 |
| Problem 22: Names scores | 22_names_scores.py | 871198282 |
| Problem 23: Non-abundant sums | 23_non_abundant_sums.py | 4179871 |
| Problem 24: Lexicographic permutations | ||
| Problem 25: 1000-digit Fibonacci number | ||
| Problem 26: Reciprocal cycles | ||
| Problem 27: Quadratic primes | ||
| Problem 28: Number spiral diagonals | ||
| Problem 29: Distinct powers | ||
| Problem 30: Digit fifth powers | ||
| Problem 31: Coin sums | ||
| Problem 32: Pandigital products | ||
| Problem 33: Digit cancelling fractions | ||
| Problem 34: Digit factorials | ||
| Problem 35: Circular primes | ||
| Problem 36: Double-base palindromes | ||
| Problem 37: Truncatable primes | ||
| Problem 38: Pandigital multiples | ||
| Problem 39: Integer right triangles | ||
| Problem 40: Champernowne's constant | ||
| Problem 41: Pandigital prime | ||
| Problem 42: Coded triangle numbers | ||
| Problem 43: Sub-string divisibility | ||
| Problem 44: Pentagon numbers | ||
| Problem 45: Triangular, pentagonal, and hexagonal | ||
| Problem 46: Goldbach's other conjecture | ||
| Problem 47: Distinct primes factors | ||
| Problem 48: Self powers | ||
| Problem 49: Prime permutations | ||
| Problem 50: Consecutive prime sum | ||
| Problem 51: Prime digit replacements | ||
| Problem 52: Permuted multiples | ||
| Problem 53: Combinatoric selections | ||
| Problem 54: Poker hands | ||
| Problem 55: Lychrel numbers | ||
| Problem 56: Powerful digit sum | ||
| Problem 57: Square root convergents | ||
| Problem 58: Spiral primes | ||
| Problem 59: XOR decryption | ||
| Problem 60: Prime pair sets | ||
| Problem 61: Cyclical figurate numbers | ||
| Problem 62: Cubic permutations | ||
| Problem 63: Powerful digit counts | ||
| Problem 64: Odd period square roots | ||
| Problem 65: Convergents of e | ||
| Problem 66: Diophantine equation | ||
| Problem 67: Maximum path sum II | ||
| Problem 68: Magic 5-gon ring | ||
| Problem 69: Totient maximum | ||
| Problem 70: Totient permutation | ||
| Problem 71: Ordered fractions | ||
| Problem 72: Counting fractions | ||
| Problem 73: Counting fractions in a range | ||
| Problem 74: Digit factorial chains | ||
| Problem 75: Singular integer right triangles | ||
| Problem 76: Counting summations | ||
| Problem 77: Prime summations | ||
| Problem 78: Coin partitions | ||
| Problem 79: Passcode derivation | ||
| Problem 80: Square root digital expansion | ||
| Problem 81: Path sum: two ways | ||
| Problem 82: Path sum: three ways | ||
| Problem 83: Path sum: four ways | ||
| Problem 84: Monopoly odds | ||
| Problem 85: Counting rectangles | ||
| Problem 86: Cuboid route | ||
| Problem 87: Prime power triples | ||
| Problem 88: Product-sum numbers | ||
| Problem 89: Roman numerals | ||
| Problem 90: Cube digit pairs | ||
| Problem 91: Right triangles with integer coordinates | ||
| Problem 92: Square digit chains | ||
| Problem 93: Arithmetic expressions | ||
| Problem 94: Almost equilateral triangles | ||
| Problem 95: Amicable chains | ||
| Problem 96: Su Doku | ||
| Problem 97: Large non-Mersenne prime | ||
| Problem 98: Anagramic squares | ||
| Problem 99: Largest exponential | ||
| Problem 100: Arranged probability | ||
| Problem 101: Optimum polynomial | ||
| Problem 102: Triangle containment | ||
| Problem 103: Special subset sums: optimum | ||
| Problem 104: Pandigital Fibonacci ends | ||
| Problem 105: Special subset sums: testing | ||
| Problem 106: Special subset sums: meta-testing | ||
| Problem 107: Minimal network | ||
| Problem 108: Diophantine reciprocals I | ||
| Problem 109: Darts | ||
| Problem 110: Diophantine reciprocals II | ||
| Problem 111: Primes with runs | ||
| Problem 112: Bouncy numbers | ||
| Problem 113: Non-bouncy numbers | ||
| Problem 114: Counting block combinations I | ||
| Problem 115: Counting block combinations II | ||
| Problem 116: Red, green or blue tiles | ||
| Problem 117: Red, green, and blue tiles | ||
| Problem 118: Pandigital prime sets | ||
| Problem 119: Digit power sum | ||
| Problem 120: Square remainders | ||
| Problem 121: Disc game prize fund | ||
| Problem 122: Efficient exponentiation | ||
| Problem 123: Prime square remainders | ||
| Problem 124: Ordered radicals | ||
| Problem 125: Palindromic sums | ||
| Problem 126: Cuboid layers | ||
| Problem 127: abc-hits | ||
| Problem 128: Hexagonal tile differences | ||
| Problem 129: Repunit divisibility | ||
| Problem 130: Composites with prime repunit property | ||
| Problem 131: Prime cube partnership | ||
| Problem 132: Large repunit factors | ||
| Problem 133: Repunit nonfactors | ||
| Problem 134: Prime pair connection | ||
| Problem 135: Same differences | ||
| Problem 136: Singleton difference | ||
| Problem 137: Fibonacci golden nuggets | ||
| Problem 138: Special isosceles triangles | ||
| Problem 139: Pythagorean tiles | ||
| Problem 140: Modified Fibonacci golden nuggets | ||
| Problem 141: Investigating progressive numbers, , which are also square | ||
| Problem 142: Perfect Square Collection | ||
| Problem 143: Investigating the Torricelli point of a triangle | ||
| Problem 144: Investigating multiple reflections of a laser beam | ||
| Problem 145: How many reversible numbers are there below one-billion? | ||
| Problem 146: Investigating a Prime Pattern | ||
| Problem 147: Rectangles in cross-hatched grids | ||
| Problem 148: Exploring Pascal's triangle | ||
| Problem 149: Searching for a maximum-sum subsequence | ||
| Problem 150: Searching a triangular array for a sub-triangle having minimum-sum | ||
| Problem 151: Paper sheets of standard sizes: an expected-value problem | ||
| Problem 152: Writing 1/2 as a sum of inverse squares | ||
| Problem 153: Investigating Gaussian Integers | ||
| Problem 154: Exploring Pascal's pyramid | ||
| Problem 155: Counting Capacitor Circuits | ||
| Problem 156: Counting Digits | ||
| Problem 157: Solving the diophantine equation /+/= / | ||
| Problem 158: Exploring strings for which only one character comes lexicographically after its neighbour to the left | ||
| Problem 159: Digital root sums of factorisations | ||
| Problem 160: Factorial trailing digits | ||
| Problem 161: Triominoes | ||
| Problem 162: Hexadecimal numbers | ||
| Problem 163: Cross-hatched triangles | ||
| Problem 164: Numbers for which no three consecutive digits have a sum greater than a given value | ||
| Problem 165: Intersections | ||
| Problem 166: Criss Cross | ||
| Problem 167: Investigating Ulam sequences | ||
| Problem 168: Number Rotations | ||
| Problem 169: Exploring the number of different ways a number can be expressed as a sum of powers of 2 | ||
| Problem 170: Find the largest 0 to 9 pandigital that can be formed by concatenating products | ||
| Problem 171: Finding numbers for which the sum of the squares of the digits is a square | ||
| Problem 172: Investigating numbers with few repeated digits | ||
| Problem 173: Using up to one million tiles how many different "hollow" square laminae can be formed? | ||
| Problem 174: Counting the number of "hollow" square laminae that can form one, two, three, ... distinct arrangements | ||
| Problem 175: Fractions involving the number of different ways a number can be expressed as a sum of powers of 2 | ||
| Problem 176: Right-angled triangles that share a cathetus | ||
| Problem 177: Integer angled Quadrilaterals | ||
| Problem 178: Step Numbers | ||
| Problem 179: Consecutive positive divisors | ||
| Problem 180: Rational zeros of a function of three variables | ||
| Problem 181: Investigating in how many ways objects of two different colours can be grouped | ||
| Problem 182: RSA encryption | ||
| Problem 183: Maximum product of parts | ||
| Problem 184: Triangles containing the origin | ||
| Problem 185: Number Mind | ||
| Problem 186: Connectedness of a network | ||
| Problem 187: Semiprimes | ||
| Problem 188: The hyperexponentiation of a number | ||
| Problem 189: Tri-colouring a triangular grid | ||
| Problem 190: Maximising a weighted product | ||
| Problem 191: Prize Strings | ||
| Problem 192: Best Approximations | ||
| Problem 193: Squarefree Numbers | ||
| Problem 194: Coloured Configurations | ||
| Problem 195: Inscribed circles of triangles with one angle of 60 degrees | ||
| Problem 196: Prime triplets | ||
| Problem 197: Investigating the behaviour of a recursively defined sequence | ||
| Problem 198: Ambiguous Numbers | ||
| Problem 199: Iterative Circle Packing | ||
| Problem 200: Find the 200th prime-proof sqube containing the contiguous sub-string "200" | ||
| Problem 201: Subsets with a unique sum | ||
| Problem 202: Laserbeam | ||
| Problem 203: Squarefree Binomial Coefficients | ||
| Problem 204: Generalised Hamming Numbers | ||
| Problem 205: Dice Game | ||
| Problem 206: Concealed Square | ||
| Problem 207: Integer partition equations | ||
| Problem 208: Robot Walks | ||
| Problem 209: Circular Logic | ||
| Problem 210: Obtuse Angled Triangles | ||
| Problem 211: Divisor Square Sum | ||
| Problem 212: Combined Volume of Cuboids | ||
| Problem 213: Flea Circus | ||
| Problem 214: Totient Chains | ||
| Problem 215: Crack-free Walls | ||
| Problem 216: Investigating the primality of numbers of the form 2-1 | ||
| Problem 217: Balanced Numbers | ||
| Problem 218: Perfect right-angled triangles | ||
| Problem 219: Skew-cost coding | ||
| Problem 220: Heighway Dragon | ||
| Problem 221: Alexandrian Integers | ||
| Problem 222: Sphere Packing | ||
| Problem 223: Almost right-angled triangles I | ||
| Problem 224: Almost right-angled triangles II | ||
| Problem 225: Tribonacci non-divisors | ||
| Problem 226: A Scoop of Blancmange | ||
| Problem 227: The Chase | ||
| Problem 228: Minkowski Sums | ||
| Problem 229: Four Representations using Squares | ||
| Problem 230: Fibonacci Words | ||
| Problem 231: The prime factorisation of binomial coefficients | ||
| Problem 232: The Race | ||
| Problem 233: Lattice points on a circle | ||
| Problem 234: Semidivisible numbers | ||
| Problem 235: An Arithmetic Geometric sequence | ||
| Problem 236: Luxury Hampers | ||
| Problem 237: Tours on a 4 x n playing board | ||
| Problem 238: Infinite string tour | ||
| Problem 239: Twenty-two Foolish Primes | ||
| Problem 240: Top Dice | ||
| Problem 241: Perfection Quotients | ||
| Problem 242: Odd Triplets | ||
| Problem 243: Resilience | ||
| Problem 244: Sliders | ||
| Problem 245: Coresilience | ||
| Problem 246: Tangents to an ellipse | ||
| Problem 247: Squares under a hyperbola | ||
| Problem 248: Numbers for which Euler’s totient function equals 13! | ||
| Problem 249: Prime Subset Sums | ||
| Problem 250: 250250 | ||
| Problem 251: Cardano Triplets | ||
| Problem 252: Convex Holes | ||
| Problem 253: Tidying up | ||
| Problem 254: Sums of Digit Factorials | ||
| Problem 255: Rounded Square Roots | ||
| Problem 256: Tatami-Free Rooms | ||
| Problem 257: Angular Bisectors | ||
| Problem 258: A lagged Fibonacci sequence | ||
| Problem 259: Reachable Numbers | ||
| Problem 260: Stone Game | ||
| Problem 261: Pivotal Square Sums | ||
| Problem 262: Mountain Range | ||
| Problem 263: An engineers' dream come true | ||
| Problem 264: Triangle Centres | ||
| Problem 265: Binary Circles | ||
| Problem 266: Pseudo Square Root | ||
| Problem 267: Billionaire | ||
| Problem 268: Counting numbers with at least four distinct prime factors less than 100 | ||
| Problem 269: Polynomials with at least one integer root | ||
| Problem 270: Cutting Squares | ||
| Problem 271: Modular Cubes, part 1 | ||
| Problem 272: Modular Cubes, part 2 | ||
| Problem 273: Sum of Squares | ||
| Problem 274: Divisibility Multipliers | ||
| Problem 275: Balanced Sculptures | ||
| Problem 276: Primitive Triangles | ||
| Problem 277: A Modified Collatz sequence | ||
| Problem 278: Linear Combinations of Semiprimes | ||
| Problem 279: Triangles with integral sides and an integral angle | ||
| Problem 280: Ant and seeds | ||
| Problem 281: Pizza Toppings | ||
| Problem 282: The Ackermann function | ||
| Problem 283: Integer sided triangles for which the area/perimeter ratio is integral | ||
| Problem 284: Steady Squares | ||
| Problem 285: Pythagorean odds | ||
| Problem 286: Scoring probabilities | ||
| Problem 287: Quadtree encoding (a simple compression algorithm) | ||
| Problem 288: An enormous factorial | ||
| Problem 289: Eulerian Cycles | ||
| Problem 290: Digital Signature | ||
| Problem 291: Panaitopol Primes | ||
| Problem 292: Pythagorean Polygons | ||
| Problem 293: Pseudo-Fortunate Numbers | ||
| Problem 294: Sum of digits - experience #23 | ||
| Problem 295: Lenticular holes | ||
| Problem 296: Angular Bisector and Tangent | ||
| Problem 297: Zeckendorf Representation | ||
| Problem 298: Selective Amnesia | ||
| Problem 299: Three similar triangles | ||
| Problem 300: Protein folding | ||
| Problem 301: Nim | ||
| Problem 302: Strong Achilles Numbers | ||
| Problem 303: Multiples with small digits | ||
| Problem 304: Primonacci | ||
| Problem 305: Reflexive Position | ||
| Problem 306: Paper-strip Game | ||
| Problem 307: Chip Defects | ||
| Problem 308: An amazing Prime-generating Automaton | ||
| Problem 309: Integer Ladders | ||
| Problem 310: Nim Square | ||
| Problem 311: Biclinic Integral Quadrilaterals | ||
| Problem 312: Cyclic paths on Sierpiński graphs | ||
| Problem 313: Sliding game | ||
| Problem 314: The Mouse on the Moon | ||
| Problem 315: Digital root clocks | ||
| Problem 316: Numbers in decimal expansions | ||
| Problem 317: Firecracker | ||
| Problem 318: 2011 nines | ||
| Problem 319: Bounded Sequences | ||
| Problem 320: Factorials divisible by a huge integer | ||
| Problem 321: Swapping Counters | ||
| Problem 322: Binomial coefficients divisible by 10 | ||
| Problem 323: Bitwise-OR operations on random integers | ||
| Problem 324: Building a tower | ||
| Problem 325: Stone Game II | ||
| Problem 326: Modulo Summations | ||
| Problem 327: Rooms of Doom | ||
| Problem 328: Lowest-cost Search | ||
| Problem 329: Prime Frog | ||
| Problem 330: Euler's Number | ||
| Problem 331: Cross flips | ||
| Problem 332: Spherical triangles | ||
| Problem 333: Special partitions | ||
| Problem 334: Spilling the beans | ||
| Problem 335: Gathering the beans | ||
| Problem 336: Maximix Arrangements | ||
| Problem 337: Totient Stairstep Sequences | ||
| Problem 338: Cutting Rectangular Grid Paper | ||
| Problem 339: Peredur fab Efrawg | ||
| Problem 340: Crazy Function | ||
| Problem 341: Golomb's self-describing sequence | ||
| Problem 342: The totient of a square is a cube | ||
| Problem 343: Fractional Sequences | ||
| Problem 344: Silver dollar game | ||
| Problem 345: Matrix Sum | ||
| Problem 346: Strong Repunits | ||
| Problem 347: Largest integer divisible by two primes | ||
| Problem 348: Sum of a square and a cube | ||
| Problem 349: Langton's ant | ||
| Problem 350: Constraining the least greatest and the greatest least | ||
| Problem 351: Hexagonal orchards | ||
| Problem 352: Blood tests | ||
| Problem 353: Risky moon | ||
| Problem 354: Distances in a bee's honeycomb | ||
| Problem 355: Maximal coprime subset | ||
| Problem 356: Largest roots of cubic polynomials | ||
| Problem 357: Prime generating integers | ||
| Problem 358: Cyclic numbers | ||
| Problem 359: Hilbert's New Hotel | ||
| Problem 360: Scary Sphere | ||
| Problem 361: Subsequence of Thue-Morse sequence | ||
| Problem 362: Squarefree factors | ||
| Problem 363: Bézier Curves | ||
| Problem 364: Comfortable distance | ||
| Problem 365: A huge binomial coefficient | ||
| Problem 366: Stone Game III | ||
| Problem 367: Bozo sort | ||
| Problem 368: A Kempner-like series | ||
| Problem 369: Badugi | ||
| Problem 370: Geometric triangles | ||
| Problem 371: Licence plates | ||
| Problem 372: Pencils of rays | ||
| Problem 373: Circumscribed Circles | ||
| Problem 374: Maximum Integer Partition Product | ||
| Problem 375: Minimum of subsequences | ||
| Problem 376: Nontransitive sets of dice | ||
| Problem 377: Sum of digits, experience 13 | ||
| Problem 378: Triangle Triples | ||
| Problem 379: Least common multiple count | ||
| Problem 380: Amazing Mazes! | ||
| Problem 381: (prime-k) factorial | ||
| Problem 382: Generating polygons | ||
| Problem 383: Divisibility comparison between factorials | ||
| Problem 384: Rudin-Shapiro sequence | ||
| Problem 385: Ellipses inside triangles | ||
| Problem 386: Maximum length of an antichain | ||
| Problem 387: Harshad Numbers | ||
| Problem 388: Distinct Lines | ||
| Problem 389: Platonic Dice | ||
| Problem 390: Triangles with non rational sides and integral area | ||
| Problem 391: Hopping Game | ||
| Problem 392: Enmeshed unit circle | ||
| Problem 393: Migrating ants | ||
| Problem 394: Eating pie | ||
| Problem 395: Pythagorean tree | ||
| Problem 396: Weak Goodstein sequence | ||
| Problem 397: Triangle on parabola | ||
| Problem 398: Cutting rope | ||
| Problem 399: Squarefree Fibonacci Numbers | ||
| Problem 400: Fibonacci tree game | ||
| Problem 401: Sum of squares of divisors | ||
| Problem 402: Integer-valued polynomials | ||
| Problem 403: Lattice points enclosed by parabola and line | ||
| Problem 404: Crisscross Ellipses | ||
| Problem 405: A rectangular tiling | ||
| Problem 406: Guessing Game | ||
| Problem 407: Idempotents | ||
| Problem 408: Admissible paths through a grid | ||
| Problem 409: Nim Extreme | ||
| Problem 410: Circle and tangent line | ||
| Problem 411: Uphill paths | ||
| Problem 412: Gnomon numbering | ||
| Problem 413: One-child Numbers | ||
| Problem 414: Kaprekar constant | ||
| Problem 415: Titanic sets | ||
| Problem 416: A frog's trip | ||
| Problem 417: Reciprocal cycles II | ||
| Problem 418: Factorisation triples | ||
| Problem 419: Look and say sequence | ||
| Problem 420: 2x2 positive integer matrix | ||
| Problem 421: Prime factors of +1 | ||
| Problem 422: Sequence of points on a hyperbola | ||
| Problem 423: Consecutive die throws | ||
| Problem 424: Kakuro | ||
| Problem 425: Prime connection | ||
| Problem 426: Box-ball system | ||
| Problem 427: n-sequences | ||
| Problem 428: Necklace of circles | ||
| Problem 429: Sum of squares of unitary divisors | ||
| Problem 430: Range flips | ||
| Problem 431: Square Space Silo | ||
| Problem 432: Totient sum | ||
| Problem 433: Steps in Euclid's algorithm | ||
| Problem 434: Rigid graphs | ||
| Problem 435: Polynomials of Fibonacci numbers | ||
| Problem 436: Unfair wager | ||
| Problem 437: Fibonacci primitive roots | ||
| Problem 438: Integer part of polynomial equation's solutions | ||
| Problem 439: Sum of sum of divisors | ||
| Problem 440: GCD and Tiling | ||
| Problem 441: The inverse summation of coprime couples | ||
| Problem 442: Eleven-free integers | ||
| Problem 443: GCD sequence | ||
| Problem 444: The Roundtable Lottery | ||
| Problem 445: Retractions A | ||
| Problem 446: Retractions B | ||
| Problem 447: Retractions C | ||
| Problem 448: Average least common multiple | ||
| Problem 449: Chocolate covered candy | ||
| Problem 450: Hypocycloid and Lattice points | ||
| Problem 451: Modular inverses | ||
| Problem 452: Long Products | ||
| Problem 453: Lattice Quadrilaterals | ||
| Problem 454: Diophantine reciprocals III | ||
| Problem 455: Powers With Trailing Digits | ||
| Problem 456: Triangles containing the origin II | ||
| Problem 457: A polynomial modulo the square of a prime | ||
| Problem 458: Permutations of Project | ||
| Problem 459: Flipping game | ||
| Problem 460: An ant on the move | ||
| Problem 461: Almost Pi | ||
| Problem 462: Permutation of 3-smooth numbers | ||
| Problem 463: A weird recurrence relation | ||
| Problem 464: Möbius function and intervals | ||
| Problem 465: Polar polygons | ||
| Problem 466: Distinct terms in a multiplication table | ||
| Problem 467: Superinteger | ||
| Problem 468: Smooth divisors of binomial coefficients | ||
| Problem 469: Empty chairs | ||
| Problem 470: Super Ramvok | ||
| Problem 471: Triangle inscribed in ellipse | ||
| Problem 472: Comfortable Distance II | ||
| Problem 473: Phigital number base | ||
| Problem 474: Last digits of divisors | ||
| Problem 475: Music festival | ||
| Problem 476: Circle Packing II | ||
| Problem 477: Number Sequence Game | ||
| Problem 478: Mixtures | ||
| Problem 479: Roots on the Rise | ||
| Problem 480: The Last Question | ||
| Problem 481: Chef Showdown | ||
| Problem 482: The incenter of a triangle | ||
| Problem 483: Repeated permutation | ||
| Problem 484: Arithmetic Derivative | ||
| Problem 485: Maximum number of divisors | ||
| Problem 486: Palindrome-containing strings | ||
| Problem 487: Sums of power sums | ||
| Problem 488: Unbalanced Nim | ||
| Problem 489: Common factors between two sequences | ||
| Problem 490: Jumping frog | ||
| Problem 491: Double pandigital number divisible by 11 | ||
| Problem 492: Exploding sequence | ||
| Problem 493: Under The Rainbow | ||
| Problem 494: Collatz prefix families | ||
| Problem 495: Writing n as the product of k distinct positive integers | ||
| Problem 496: Incenter and circumcenter of triangle | ||
| Problem 497: Drunken Tower of Hanoi | ||
| Problem 498: Remainder of polynomial division | ||
| Problem 499: St. Petersburg Lottery | ||
| Problem 500: Problem 500!!! | ||
| Problem 501: Eight Divisors | ||
| Problem 502: Counting Castles | ||
| Problem 503: Compromise or persist | ||
| Problem 504: Square on the Inside | ||
| Problem 505: Bidirectional Recurrence | ||
| Problem 506: Clock sequence | ||
| Problem 507: Shortest Lattice Vector | ||
| Problem 508: Integers in base i-1 | ||
| Problem 509: Divisor Nim | ||
| Problem 510: Tangent Circles | ||
| Problem 511: Sequences with nice divisibility properties | ||
| Problem 512: Sums of totients of powers | ||
| Problem 513: Integral median | ||
| Problem 514: Geoboard Shapes | ||
| Problem 515: Dissonant Numbers | ||
| Problem 516: 5-smooth totients | ||
| Problem 517: A real recursion | ||
| Problem 518: Prime triples and geometric sequences | ||
| Problem 519: Tricoloured Coin Fountains | ||
| Problem 520: Simbers | ||
| Problem 521: Smallest prime factor | ||
| Problem 522: Hilbert's Blackout | ||
| Problem 523: First Sort I | ||
| Problem 524: First Sort II | ||
| Problem 525: Rolling Ellipse | ||
| Problem 526: Largest prime factors of consecutive numbers | ||
| Problem 527: Randomized Binary Search | ||
| Problem 528: Constrained Sums | ||
| Problem 529: 10-substrings | ||
| Problem 530: GCD of Divisors | ||
| Problem 531: Chinese leftovers | ||
| Problem 532: Nanobots on Geodesics | ||
| Problem 533: Minimum values of the Carmichael function | ||
| Problem 534: Weak Queens | ||
| Problem 535: Fractal Sequence | ||
| Problem 536: Modulo power identity | ||
| Problem 537: Counting tuples | ||
| Problem 538: Maximum quadrilaterals | ||
| Problem 539: Odd elimination | ||
| Problem 540: Counting primitive Pythagorean triples | ||
| Problem 541: Divisibility of Harmonic Number Denominators | ||
| Problem 542: Geometric Progression with Maximum Sum | ||
| Problem 543: Prime-Sum Numbers | ||
| Problem 544: Chromatic Conundrum | ||
| Problem 545: Faulhaber's Formulas | ||
| Problem 546: The Floor's Revenge | ||
| Problem 547: Distance of random points within hollow square laminae | ||
| Problem 548: Gozinta Chains | ||
| Problem 549: Divisibility of factorials | ||
| Problem 550: Divisor game | ||
| Problem 551: Sum of digits sequence | ||
| Problem 552: Chinese leftovers II | ||
| Problem 553: Power sets of power sets | ||
| Problem 554: Centaurs on a chess board | ||
| Problem 555: McCarthy 91 function | ||
| Problem 556: Squarefree Gaussian Integers | ||
| Problem 557: Cutting triangles | ||
| Problem 558: Irrational base | ||
| Problem 559: Permuted Matrices | ||
| Problem 560: Coprime Nim | ||
| Problem 561: Divisor Pairs | ||
| Problem 562: Maximal perimeter | ||
| Problem 563: Robot Welders | ||
| Problem 564: Maximal polygons | ||
| Problem 565: Divisibility of sum of divisors | ||
| Problem 566: Cake Icing Puzzle | ||
| Problem 567: Reciprocal games I | ||
| Problem 568: Reciprocal games II | ||
| Problem 569: Prime Mountain Range | ||
| Problem 570: Snowflakes | ||
| Problem 571: Super Pandigital Numbers | ||
| Problem 572: Idempotent matrices | ||
| Problem 573: Unfair race | ||
| Problem 574: Verifying Primes | ||
| Problem 575: Wandering Robots | ||
| Problem 576: Irrational jumps | ||
| Problem 577: Counting hexagons | ||
| Problem 578: Integers with decreasing prime powers | ||
| Problem 579: Lattice points in lattice cubes | ||
| Problem 580: Squarefree Hilbert numbers | ||
| Problem 581: 47-smooth triangular numbers | ||
| Problem 582: Nearly isosceles 120 degree triangles | ||
| Problem 583: Heron Envelopes | ||
| Problem 584: Birthday Problem Revisited | ||
| Problem 585: Nested square roots | ||
| Problem 586: Binary Quadratic Form | ||
| Problem 587: Concave triangle | ||
| Problem 588: Quintinomial coefficients | ||
| Problem 589: Poohsticks Marathon | ||
| Problem 590: Sets with a given Least Common Multiple | ||
| Problem 591: Best Approximations by Quadratic Integers | ||
| Problem 592: Factorial trailing digits 2 | ||
| Problem 593: Fleeting Medians | ||
| Problem 594: Rhombus Tilings | ||
| Problem 595: Incremental Random Sort | ||
| Problem 596: Number of lattice points in a hyperball | ||
| Problem 597: Torpids | ||
| Problem 598: Split Divisibilities | ||
| Problem 599: Distinct Colourings of a Rubik's Cube | ||
| Problem 600: Integer sided equiangular hexagons | ||
| Problem 601: Divisibility streaks | ||
| Problem 602: Product of Head Counts | ||
| Problem 603: Substring sums of prime concatenations | ||
| Problem 604: Convex path in square | ||
| Problem 605: Pairwise Coin-Tossing Game | ||
| Problem 606: Gozinta Chains II | ||
| Problem 607: Marsh Crossing | ||
| Problem 608: Divisor Sums | ||
| Problem 609: π sequences | ||
| Problem 610: Roman Numerals II | ||
| Problem 611: Hallway of square steps | ||
| Problem 612: Friend numbers | ||
| Problem 613: Pythagorean Ant | ||
| Problem 614: Special partitions 2 | ||
| Problem 615: The millionth number with at least one million prime factors | ||
| Problem 616: Creative numbers | ||
| Problem 617: Mirror Power Sequence | ||
| Problem 618: Numbers with a given prime factor sum | ||
| Problem 619: Square subsets | ||
| Problem 620: Planetary Gears | ||
| Problem 621: Expressing an integer as the sum of triangular numbers | ||
| Problem 622: Riffle Shuffles | ||
| Problem 623: Lambda Count | ||
| Problem 624: Two heads are better than one | ||
| Problem 625: Gcd sum | ||
| Problem 626: Counting Binary Matrices | ||
| Problem 627: Counting products | ||
| Problem 628: Open chess positions | ||
| Problem 629: Scatterstone Nim | ||
| Problem 630: Crossed lines | ||
| Problem 631: Constrained Permutations | ||
| Problem 632: Square prime factors | ||
| Problem 633: Square prime factors II | ||
| Problem 634: Numbers of the form |
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| Problem 635: Subset sums | ||
| Problem 636: Restricted Factorisations | ||
| Problem 637: Flexible digit sum | ||
| Problem 638: Weighted lattice paths | ||
| Problem 639: Summing a multiplicative function | ||
| Problem 640: Shut the Box | ||
| Problem 641: A Long Row of Dice | ||
| Problem 642: Sum of largest prime factors | ||
| Problem 643: 2-Friendly | ||
| Problem 644: Squares on the line | ||
| Problem 645: Every Day is a Holiday | ||
| Problem 646: Bounded Divisors | ||
| Problem 647: Linear Transformations of Polygonal Numbers | ||
| Problem 648: Skipping Squares | ||
| Problem 649: Low-Prime Chessboard Nim | ||
| Problem 650: Divisors of Binomial Product | ||
| Problem 651: Patterned Cylinders | ||
| Problem 652: Distinct values of a proto-logarithmic function | ||
| Problem 653: Frictionless Tube | ||
| Problem 654: Neighbourly Constraints | ||
| Problem 655: Divisible Palindromes | ||
| Problem 656: Palindromic sequences | ||
| Problem 657: Incomplete words | ||
| Problem 658: Incomplete words II | ||
| Problem 659: Largest prime | ||
| Problem 660: Pandigital Triangles | ||
| Problem 661: A Long Chess Match | ||
| Problem 662: Fibonacci paths | ||
| Problem 663: Sums of subarrays | ||
| Problem 664: An infinite game | ||
| Problem 665: Proportionate Nim | ||
| Problem 666: Polymorphic Bacteria | ||
| Problem 667: Moving Pentagon | ||
| Problem 668: Square root smooth Numbers | ||
| Problem 669: The King's Banquet | ||
| Problem 670: Colouring a Strip | ||
| Problem 671: Colouring a Loop | ||
| Problem 672: One more one | ||
| Problem 673: Beds and Desks | ||
| Problem 674: Solving |
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| Problem 675: |
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| Problem 676: Matching Digit Sums | ||
| Problem 677: Coloured Graphs | ||
| Problem 678: Fermat-like Equations | ||
| Problem 679: Freefarea | ||
| Problem 680: Yarra Gnisrever | ||
| Problem 681: Maximal Area | ||
| Problem 682: 5-Smooth Pairs | ||
| Problem 683: The Chase II | ||
| Problem 684: Inverse Digit Sum | ||
| Problem 685: Inverse Digit Sum II | ||
| Problem 686: Powers of Two | ||
| Problem 687: Shuffling Cards | ||
| Problem 688: Piles of Plates | ||
| Problem 689: Binary Series | ||
| Problem 690: Tom and Jerry | ||
| Problem 691: Long substring with many repetitions |