Project Euler

What is the Project Euler?

Project Euler is a series of challenging math/computer programming problems that will require more than just mathematical understanding to solve.

While math will help you come up with elegant and efficient methods, the use of a computer and programming skills will be needed to solve most problems.

Who are the problems for?

The intended audience include students whose curiosity goes beyond the traditional curriculum, seeking enriching challenges, adults whose training was not predominantly in the area of Mathematics, but who find fascination in subjects related to it.

In addition, professionals determined to keep their problem-solving skills and their affinity for Mathematics at the forefront.

As of the date of this publication or its last update, Project Euler has a remarkable community, surpassing 1,250,000 million registered members, who have solved at least one problem.

Additionally, registered members represent 220 locations around the world, and are collectively using 112 different programming languages to solve problems.

Can anyone solve the problems?

The range of challenges presents variations in difficulty, and for many, the experience is an inductive cascading learning process. In other words, solving a problem opens doors to new concepts, which in turn allow solving previously inaccessible challenges. Therefore, the dedicated participant will advance gradually but steadily, overcoming the proposed problems one by one.

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

About this series

In order to improve my math/computer programming problem solving skills, I will start a series of posts where each one will be the presentation, solution and explanation of a problem.

What challenges have already been resolved?

All the challenges below were taken from the Project Euler and freeCodeCamp archives, whenever I solve a problem I will update this list.

Problems 1 to 100

In this first set of challenges, you will use mathematical concepts like the Fibonacci sequence, prime number theory, and combinatorics to write efficient algorithms to solve these problems.

Problem 1: Multiples of 3 and 5
Problem 2: Even Fibonacci Numbers
Problem 3: Largest prime factor
Problem 4: Largest palindrome product
Problem 5: Smallest multiple
Problem 6: Sum square difference
Problem 7: 10001st prime
Problem 8: Largest product in a series
Problem 9: Special Pythagorean triplet
Problem 10: Summation of primes
Problem 11: Largest product in a grid
Problem 12: Highly divisible triangular number
Problem 13: Large sum
Problem 14: Longest Collatz sequence
Problem 15: Lattice paths
Problem 16: Power digit sum
Problem 17: Number letter counts
Problem 18: Maximum path sum I
Problem 19: Counting Sundays
Problem 20: Factorial digit sum
Problem 21: Amicable numbers
Problem 22: Names scores
Problem 23: Non-abundant sums
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 n 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

Problems 101 to 200

In this set of challenges, you will build upon the skills you learned in the first part of the course and use more advanced concepts like vector computation, Pascal's pyramid, and the RSA algorithm to solve these problems efficiently.

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, n, 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 one half 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"

Problems 201 to 300

In this set of challenges, you will continue to build upon the skills you learned earlier and use concepts like the binomial theorem, Hamming numbers, and the Collatz sequence to further develop your math and problems solving skills.

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 2n2-1
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

Problems 301 to 400

Here you will continue to flex your mathematical and algorithmic skills as you use concepts such as combinatorial game theory, bitwise operations, and Golomb's self-describing sequence to develop efficient solutions to these problems.

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

Problems 401 to 500

In this final set of challenges, you will need draw upon everything you learned up to this point and use advanced concepts like unitary divisors, the Kaprekar routine, and much more to solve these complex problems.

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 n^15+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!!!

For now, these are the problems I want to solve and post here, I will update the list as I solve them.

References

Thanks for reading this far and see you in the upcoming posts! 👋
Happy coding! 🚀