Project Euler

What is Project Euler?

Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems. (Project Euler)

Problem 1: Multiples of 3 and 5Problem 2: Even Fibonacci NumbersProblem 3: Largest prime factorProblem 4: Largest palindrome productProblem 5: Smallest multipleProblem 6: Sum square differenceProblem 7: 10001st primeProblem 8: Largest product in a seriesProblem 9: Special Pythagorean tripletProblem 10: Summation of primesProblem 11: Largest product in a gridProblem 12: Highly divisible triangular numberProblem 13: Large sumProblem 14: Longest Collatz sequenceProblem 15: Lattice pathsProblem 16: Power digit sumProblem 17: Number letter countsProblem 18: Maximum path sum IProblem 19: Counting SundaysProblem 20: Factorial digit sumProblem 21: Amicable numbersProblem 22: Names scoresProblem 23: Non-abundant sumsProblem 24: Lexicographic permutationsProblem 25: 1000-digit Fibonacci numberProblem 26: Reciprocal cyclesProblem 27: Quadratic primesProblem 28: Number spiral diagonalsProblem 29: Distinct powersProblem 30: Digit n powersProblem 31: Coin sumsProblem 32: Pandigital productsProblem 33: Digit cancelling fractionsProblem 34: Digit factorialsProblem 35: Circular primesProblem 36: Double-base palindromesProblem 37: Truncatable primesProblem 38: Pandigital multiplesProblem 39: Integer right trianglesProblem 40: Champernowne's constantProblem 41: Pandigital primeProblem 42: Coded triangle numbersProblem 43: Sub-string divisibilityProblem 44: Pentagon numbersProblem 45: Triangular, pentagonal, and hexagonalProblem 46: Goldbach's other conjectureProblem 47: Distinct primes factorsProblem 48: Self powersProblem 49: Prime permutationsProblem 50: Consecutive prime sumProblem 51: Prime digit replacementsProblem 52: Permuted multiplesProblem 53: Combinatoric selectionsProblem 54: Poker handsProblem 55: Lychrel numbersProblem 56: Powerful digit sumProblem 57: Square root convergentsProblem 58: Spiral primesProblem 59: XOR decryptionProblem 60: Prime pair setsProblem 61: Cyclical figurate numbersProblem 62: Cubic permutationsProblem 63: Powerful digit countsProblem 64: Odd period square rootsProblem 65: Convergents of eProblem 66: Diophantine equationProblem 67: Maximum path sum IIProblem 68: Magic 5-gon ringProblem 69: Totient maximumProblem 70: Totient permutationProblem 71: Ordered fractionsProblem 72: Counting fractionsProblem 73: Counting fractions in a rangeProblem 74: Digit factorial chainsProblem 75: Singular integer right trianglesProblem 76: Counting summationsProblem 77: Prime summationsProblem 78: Coin partitionsProblem 79: Passcode derivationProblem 80: Square root digital expansionProblem 81: Path sum: two waysProblem 82: Path sum: three waysProblem 83: Path sum: four waysProblem 84: Monopoly oddsProblem 85: Counting rectanglesProblem 86: Cuboid routeProblem 87: Prime power triplesProblem 88: Product-sum numbersProblem 89: Roman numeralsProblem 90: Cube digit pairsProblem 91: Right triangles with integer coordinatesProblem 92: Square digit chainsProblem 93: Arithmetic expressionsProblem 94: Almost equilateral trianglesProblem 95: Amicable chainsProblem 96: Su DokuProblem 97: Large non-Mersenne primeProblem 98: Anagramic squaresProblem 99: Largest exponentialProblem 100: Arranged probabilityProblem 101: Optimum polynomialProblem 102: Triangle containmentProblem 103: Special subset sums: optimumProblem 104: Pandigital Fibonacci endsProblem 105: Special subset sums: testingProblem 106: Special subset sums: meta-testingProblem 107: Minimal networkProblem 108: Diophantine Reciprocals IProblem 109: DartsProblem 110: Diophantine Reciprocals IIProblem 111: Primes with runsProblem 112: Bouncy numbersProblem 113: Non-bouncy numbersProblem 114: Counting block combinations IProblem 115: Counting block combinations IIProblem 116: Red, green or blue tilesProblem 117: Red, green, and blue tilesProblem 118: Pandigital prime setsProblem 119: Digit power sumProblem 120: Square remaindersProblem 121: Disc game prize fundProblem 122: Efficient exponentiationProblem 123: Prime square remaindersProblem 124: Ordered radicalsProblem 125: Palindromic sumsProblem 126: Cuboid layersProblem 127: abc-hitsProblem 128: Hexagonal tile differencesProblem 129: Repunit divisibilityProblem 130: Composites with prime repunit propertyProblem 131: Prime cube partnershipProblem 132: Large repunit factorsProblem 133: Repunit nonfactorsProblem 134: Prime pair connectionProblem 135: Same differencesProblem 136: Singleton differenceProblem 137: Fibonacci golden nuggetsProblem 138: Special isosceles trianglesProblem 139: Pythagorean tilesProblem 140: Modified Fibonacci golden nuggetsProblem 141: Investigating progressive numbers, n, which are also squareProblem 142: Perfect Square CollectionProblem 143: Investigating the Torricelli point of a triangleProblem 144: Investigating multiple reflections of a laser beamProblem 145: How many reversible numbers are there below one-billion?Problem 146: Investigating a Prime PatternProblem 147: Rectangles in cross-hatched gridsProblem 148: Exploring Pascal's triangleProblem 149: Searching for a maximum-sum subsequenceProblem 150: Searching a triangular array for a sub-triangle having minimum-sumProblem 151: Paper sheets of standard sizes: an expected-value problemProblem 152: Writing one half as a sum of inverse squaresProblem 153: Investigating Gaussian IntegersProblem 154: Exploring Pascal's pyramidProblem 155: Counting Capacitor CircuitsProblem 156: Counting DigitsProblem 157: Solving the diophantine equationProblem 158: Exploring strings for which only one character comes lexicographically after its neighbour to the leftProblem 159: Digital root sums of factorisationsProblem 160: Factorial trailing digitsProblem 161: TriominoesProblem 162: Hexadecimal numbersProblem 163: Cross-hatched trianglesProblem 164: Numbers for which no three consecutive digits have a sum greater than a given valueProblem 165: IntersectionsProblem 166: Criss CrossProblem 167: Investigating Ulam sequencesProblem 168: Number RotationsProblem 169: Exploring the number of different ways a number can be expressed as a sum of powers of 2Problem 170: Find the largest 0 to 9 pandigital that can be formed by concatenating productsProblem 171: Finding numbers for which the sum of the squares of the digits is a squareProblem 172: Investigating numbers with few repeated digitsProblem 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 arrangementsProblem 175: Fractions involving the number of different ways a number can be expressed as a sum of powers of 2Problem 176: Right-angled triangles that share a cathetusProblem 177: Integer angled QuadrilateralsProblem 178: Step NumbersProblem 179: Consecutive positive divisorsProblem 180: Rational zeros of a function of three variablesProblem 181: Investigating in how many ways objects of two different colours can be groupedProblem 182: RSA encryptionProblem 183: Maximum product of partsProblem 184: Triangles containing the originProblem 185: Number MindProblem 186: Connectedness of a networkProblem 187: SemiprimesProblem 188: The hyperexponentiation of a numberProblem 189: Tri-colouring a triangular gridProblem 190: Maximising a weighted productProblem 191: Prize StringsProblem 192: Best ApproximationsProblem 193: Squarefree NumbersProblem 194: Coloured ConfigurationsProblem 195: Inscribed circles of triangles with one angle of 60 degreesProblem 196: Prime tripletsProblem 197: Investigating the behaviour of a recursively defined sequenceProblem 198: Ambiguous NumbersProblem 199: Iterative Circle PackingProblem 200: Find the 200th prime-proof sqube containing the contiguous sub-string "200"Problem 201: Subsets with a unique sumProblem 202: LaserbeamProblem 203: Squarefree Binomial CoefficientsProblem 204: Generalised Hamming NumbersProblem 205: Dice GameProblem 206: Concealed SquareProblem 207: Integer partition equationsProblem 208: Robot WalksProblem 209: Circular LogicProblem 210: Obtuse Angled TrianglesProblem 211: Divisor Square SumProblem 212: Combined Volume of CuboidsProblem 213: Flea CircusProblem 214: Totient ChainsProblem 215: Crack-free WallsProblem 216: Investigating the primality of numbers of the form 2n2-1Problem 217: Balanced NumbersProblem 218: Perfect right-angled trianglesProblem 219: Skew-cost codingProblem 220: Heighway DragonProblem 221: Alexandrian IntegersProblem 222: Sphere PackingProblem 223: Almost right-angled triangles IProblem 224: Almost right-angled triangles IIProblem 225: Tribonacci non-divisorsProblem 226: A Scoop of BlancmangeProblem 227: The ChaseProblem 228: Minkowski SumsProblem 229: Four Representations using SquaresProblem 230: Fibonacci WordsProblem 231: The prime factorisation of binomial coefficientsProblem 232: The RaceProblem 233: Lattice points on a circleProblem 234: Semidivisible numbersProblem 235: An Arithmetic Geometric sequenceProblem 236: Luxury HampersProblem 237: Tours on a 4 x n playing boardProblem 238: Infinite string tourProblem 239: Twenty-two Foolish PrimesProblem 240: Top DiceProblem 241: Perfection QuotientsProblem 242: Odd TripletsProblem 243: ResilienceProblem 244: SlidersProblem 245: CoresilienceProblem 246: Tangents to an ellipseProblem 247: Squares under a hyperbolaProblem 248: Numbers for which Euler’s totient function equals 13!Problem 249: Prime Subset SumsProblem 250: 250250Problem 251: Cardano TripletsProblem 252: Convex HolesProblem 253: Tidying upProblem 254: Sums of Digit FactorialsProblem 255: Rounded Square RootsProblem 256: Tatami-Free RoomsProblem 257: Angular BisectorsProblem 258: A lagged Fibonacci sequenceProblem 259: Reachable NumbersProblem 260: Stone GameProblem 261: Pivotal Square SumsProblem 262: Mountain RangeProblem 263: An engineers' dream come trueProblem 264: Triangle CentresProblem 265: Binary CirclesProblem 266: Pseudo Square RootProblem 267: BillionaireProblem 268: Counting numbers with at least four distinct prime factors less than 100Problem 269: Polynomials with at least one integer rootProblem 270: Cutting SquaresProblem 271: Modular Cubes, part 1Problem 272: Modular Cubes, part 2Problem 273: Sum of SquaresProblem 274: Divisibility MultipliersProblem 275: Balanced SculpturesProblem 276: Primitive TrianglesProblem 277: A Modified Collatz sequenceProblem 278: Linear Combinations of SemiprimesProblem 279: Triangles with integral sides and an integral angleProblem 280: Ant and seedsProblem 281: Pizza ToppingsProblem 282: The Ackermann functionProblem 283: Integer sided triangles for which the area * perimeter ratio is integralProblem 284: Steady SquaresProblem 285: Pythagorean oddsProblem 286: Scoring probabilitiesProblem 287: Quadtree encoding (a simple compression algorithm)Problem 288: An enormous factorialProblem 289: Eulerian CyclesProblem 290: Digital SignatureProblem 291: Panaitopol PrimesProblem 292: Pythagorean PolygonsProblem 293: Pseudo-Fortunate NumbersProblem 294: Sum of digits - experience #23Problem 295: Lenticular holesProblem 296: Angular Bisector and TangentProblem 297: Zeckendorf RepresentationProblem 298: Selective AmnesiaProblem 299: Three similar trianglesProblem 300: Protein foldingProblem 301: NimProblem 302: Strong Achilles NumbersProblem 303: Multiples with small digitsProblem 304: PrimonacciProblem 305: Reflexive PositionProblem 306: Paper-strip GameProblem 307: Chip DefectsProblem 308: An amazing Prime-generating AutomatonProblem 309: Integer LaddersProblem 310: Nim SquareProblem 311: Biclinic Integral QuadrilateralsProblem 312: Cyclic paths on Sierpiński graphsProblem 313: Sliding gameProblem 314: The Mouse on the MoonProblem 315: Digital root clocksProblem 316: Numbers in decimal expansionsProblem 317: FirecrackerProblem 318: 2011 ninesProblem 319: Bounded SequencesProblem 320: Factorials divisible by a huge integerProblem 321: Swapping CountersProblem 322: Binomial coefficients divisible by 10Problem 323: Bitwise-OR operations on random integersProblem 324: Building a towerProblem 325: Stone Game IIProblem 326: Modulo SummationsProblem 327: Rooms of DoomProblem 328: Lowest-cost SearchProblem 329: Prime FrogProblem 330: Euler's NumberProblem 331: Cross flipsProblem 332: Spherical trianglesProblem 333: Special partitionsProblem 334: Spilling the beansProblem 335: Gathering the beansProblem 336: Maximix ArrangementsProblem 337: Totient Stairstep SequencesProblem 338: Cutting Rectangular Grid PaperProblem 339: Peredur fab EfrawgProblem 340: Crazy FunctionProblem 341: Golomb's self-describing sequenceProblem 342: The totient of a square is a cubeProblem 343: Fractional SequencesProblem 344: Silver dollar gameProblem 345: Matrix SumProblem 346: Strong RepunitsProblem 347: Largest integer divisible by two primesProblem 348: Sum of a square and a cubeProblem 349: Langton's antProblem 350: Constraining the least greatest and the greatest leastProblem 351: Hexagonal orchardsProblem 352: Blood testsProblem 353: Risky moonProblem 354: Distances in a bee's honeycombProblem 355: Maximal coprime subsetProblem 356: Largest roots of cubic polynomialsProblem 357: Prime generating integersProblem 358: Cyclic numbersProblem 359: Hilbert's New HotelProblem 360: Scary SphereProblem 361: Subsequence of Thue-Morse sequenceProblem 362: Squarefree factorsProblem 363: Bézier CurvesProblem 364: Comfortable distanceProblem 365: A huge binomial coefficientProblem 366: Stone Game IIIProblem 367: Bozo sortProblem 368: A Kempner-like seriesProblem 369: BadugiProblem 370: Geometric trianglesProblem 371: Licence platesProblem 372: Pencils of raysProblem 373: Circumscribed CirclesProblem 374: Maximum Integer Partition ProductProblem 375: Minimum of subsequencesProblem 376: Nontransitive sets of diceProblem 377: Sum of digits, experience 13Problem 378: Triangle TriplesProblem 379: Least common multiple countProblem 380: Amazing Mazes!Problem 381: (prime-k) factorialProblem 382: Generating polygonsProblem 383: Divisibility comparison between factorialsProblem 384: Rudin-Shapiro sequenceProblem 385: Ellipses inside trianglesProblem 386: Maximum length of an antichainProblem 387: Harshad NumbersProblem 388: Distinct LinesProblem 389: Platonic DiceProblem 390: Triangles with non rational sides and integral areaProblem 391: Hopping GameProblem 392: Enmeshed unit circleProblem 393: Migrating antsProblem 394: Eating pieProblem 395: Pythagorean treeProblem 396: Weak Goodstein sequenceProblem 397: Triangle on parabolaProblem 398: Cutting ropeProblem 399: Squarefree Fibonacci NumbersProblem 400: Fibonacci tree gameProblem 401: Sum of squares of divisorsProblem 402: Integer-valued polynomialsProblem 403: Lattice points enclosed by parabola and lineProblem 404: Crisscross EllipsesProblem 405: A rectangular tilingProblem 406: Guessing GameProblem 407: IdempotentsProblem 408: Admissible paths through a gridProblem 409: Nim ExtremeProblem 410: Circle and tangent lineProblem 411: Uphill pathsProblem 412: Gnomon numberingProblem 413: One-child NumbersProblem 414: Kaprekar constantProblem 415: Titanic setsProblem 416: A frog's tripProblem 417: Reciprocal cycles IIProblem 418: Factorisation triplesProblem 419: Look and say sequenceProblem 420: 2x2 positive integer matrixProblem 421: Prime factors of n15+1Problem 422: Sequence of points on a hyperbolaProblem 423: Consecutive die throwsProblem 424: KakuroProblem 425: Prime connectionProblem 426: Box-ball systemProblem 427: n-sequencesProblem 428: Necklace of CirclesProblem 429: Sum of squares of unitary divisorsProblem 430: Range flipsProblem 431: Square Space SiloProblem 432: Totient sumProblem 433: Steps in Euclid's algorithmProblem 434: Rigid graphsProblem 435: Polynomials of Fibonacci numbersProblem 436: Unfair wagerProblem 437: Fibonacci primitive rootsProblem 438: Integer part of polynomial equation's solutionsProblem 439: Sum of sum of divisorsProblem 440: GCD and TilingProblem 441: The inverse summation of coprime couplesProblem 442: Eleven-free integersProblem 443: GCD sequenceProblem 444: The Roundtable LotteryProblem 445: Retractions AProblem 446: Retractions BProblem 447: Retractions CProblem 448: Average least common multipleProblem 449: Chocolate covered candyProblem 450: Hypocycloid and Lattice pointsProblem 451: Modular inversesProblem 452: Long ProductsProblem 453: Lattice QuadrilateralsProblem 454: Diophantine reciprocals IIIProblem 455: Powers With Trailing DigitsProblem 456: Triangles containing the origin IIProblem 457: A polynomial modulo the square of a primeProblem 458: Permutations of ProjectProblem 459: Flipping gameProblem 460: An ant on the moveProblem 461: Almost PiProblem 462: Permutation of 3-smooth numbersProblem 463: A weird recurrence relationProblem 464: Möbius function and intervalsProblem 465: Polar polygonsProblem 466: Distinct terms in a multiplication tableProblem 467: SuperintegerProblem 468: Smooth divisors of binomial coefficientsProblem 469: Empty chairsProblem 470: Super RamvokProblem 471: Triangle inscribed in ellipseProblem 472: Comfortable Distance IIProblem 473: Phigital number baseProblem 474: Last digits of divisorsProblem 475: Music festivalProblem 476: Circle Packing IIProblem 477: Number Sequence GameProblem 478: MixturesProblem 479: Roots on the RiseProblem 480: The Last Question

Project Euler exists to encourage, challenge, and develop the skills and enjoyment of anyone with an interest in the fascinating world of mathematics.