"Project Euler exists to encourage, challenge, and develop the skills and enjoyment of anyone with an interest in the fascinating world of mathematics."
- Multiples of 3 and 5
- Even Fibonacci numbers
- Largest prime factor
- Largest palindrome product
- Smallest multiple
- Sum square difference
- 10001st prime
- Largest product in a series
- Special Pythagorean triplet
- Summation of primes
- Largest product in a grid
- Highly divisible triangular number
- Large sum
- Longest Collatz sequence
- Lattice paths
- Power digit sum
- Number letter counts
- Maximum path sum I
- Counting Sundays
- Factorial digit sum
- Amicable numbers
- Names scores
- Non-abundant sums
- Lexicographic permutations
- 1000-digit Fibonacci number
- Reciprocal cycles
- Quadratic primes
- Number spiral diagonals
- Distinct powers
- Digit fifth powers
- Coin sums
- Pandigital products
- Digit cancelling fractions
- Digit factorials
- Circular primes
- Double-base palindromes
- Truncatable primes
- Pandigital multiples
- Integer right triangles
- Champernowne's constant
- Pandigital prime
- Coded triangle numbers
- Sub-string divisibility
- Pentagon numbers
- Triangular, pentagonal, and hexagonal
- Goldbach's other conjecture
- Distinct primes factors
- Self powers
- Prime permutations
- Consecutive prime sum
- Prime digit replacements
- Permuted multiples
- Combinatoric selections
- Poker hands
- Lychrel numbers
- Powerful digit sum
- Square root convergents
- Spiral primes
- XOR decryption
- Prime pair sets
- Cyclical figurate numbers
- Cubic permutations
- Powerful digit counts
- Odd period square roots
- Convergents of e
- Diophantine equation
- Maximum path sum II
- Magic 5-gon ring
- Totient maximum
- Totient permutation
- Ordered fractions
- Counting fractions
- Counting fractions in a range
- Digit factorial chains
- Singular integer right triangles
- Counting summations
- Prime summations
- Coin partitions
- Passcode derivation
- Square root digital expansion
- Path sum: two ways
- Path sum: three ways
- Path sum: four ways
- Monopoly odds
- Counting rectangles
- Cuboid route
- Prime power triples
- Product-sum numbers
- Roman numerals
- Cube digit pairs
- Right triangles with integer coordinates
- Square digit chains
- Arithmetic expressions
- Almost equilateral triangles
- Amicable chains
- Su Doku
- Large non-Mersenne prime
- Anagramic squares
- Largest exponential
- Arranged probability
- Optimum polynomial
- Triangle containment
- Special subset sums: optimum
- Pandigital Fibonacci ends
- Special subset sums: testing
- Special subset sums: meta-testing
- Minimal network
- Diophantine reciprocals I
- Darts
- Diophantine reciprocals II
- Primes with runs
- Bouncy numbers
- Non-bouncy numbers
- Counting block combinations I
- Counting block combinations II
- Red, green or blue tiles
- Red, green, and blue tiles
- Pandigital prime sets
- Digit power sum
- Square remainders
- Disc game prize fund
- Efficient exponentiation
- Prime square remainders
- Ordered radicals
- Palindromic sums
- Cuboid layers
- abc-hits
- Hexagonal tile differences
- Repunit divisibility
- Composites with prime repunit property
- Prime cube partnership
- Large repunit factors
- Repunit nonfactors
- Prime pair connection
- Same differences
- Singleton difference
- Fibonacci golden nuggets
- Special isosceles triangles
- Pythagorean tiles
- Modified Fibonacci golden nuggets
- Investigating progressive numbers, n, which are also square
- Perfect Square Collection
- Investigating the Torricelli point of a triangle
- Investigating multiple reflections of a laser beam
- How many reversible numbers are there below one-billion?
- Investigating a Prime Pattern
- Rectangles in cross-hatched grids
- Exploring Pascal's triangle
- Searching for a maximum-sum subsequence
- Searching a triangular array for a sub-triangle having minimum-sum
- Paper sheets of standard sizes: an expected-value problem
- Writing 1/2 as a sum of inverse squares
- Investigating Gaussian Integers
- Exploring Pascal's pyramid
- Counting Capacitor Circuits
- Counting Digits
- Solving the diophantine equation 1/a+1/b= p/10n
- Exploring strings for which only one character comes lexicographically after its neighbour to the left
- Digital root sums of factorisations
- Factorial trailing digits
- Triominoes
- Hexadecimal numbers
- Cross-hatched triangles
- Numbers for which no three consecutive digits have a sum greater than a given value
- Intersections
- Criss Cross
- Investigating Ulam sequences
- Number Rotations
- Exploring the number of different ways a number can be expressed as a sum of powers of 2
- Find the largest 0 to 9 pandigital that can be formed by concatenating products
- Finding numbers for which the sum of the squares of the digits is a square
- Investigating numbers with few repeated digits
- Using up to one million tiles how many different "hollow" square laminae can be formed?
- Counting the number of "hollow" square laminae that can form one, two, three, ... distinct arrangements
- Fractions involving the number of different ways a number can be expressed as a sum of powers of 2
- Right-angled triangles that share a cathetus
- Integer angled Quadrilaterals
- Step Numbers
- Consecutive positive divisors
- Rational zeros of a function of three variables
- Investigating in how many ways objects of two different colours can be grouped
- RSA encryption
- Maximum product of parts
- Triangles containing the origin
- Number Mind
- Connectedness of a network
- Semiprimes
- The hyperexponentiation of a number
- Tri-colouring a triangular grid
- Maximising a weighted product
- Prize Strings
- Best Approximations
- Squarefree Numbers
- Coloured Configurations
- Inscribed circles of triangles with one angle of 60 degrees
- Prime triplets
- Investigating the behaviour of a recursively defined sequence
- Ambiguous Numbers
- Iterative Circle Packing
- Find the 200th prime-proof sqube containing the contiguous sub-string "200"
- Subsets with a unique sum
- Laserbeam
- Squarefree Binomial Coefficients
- Generalised Hamming Numbers
- Dice Game
- Concealed Square
- Integer partition equations
- Robot Walks
- Circular Logic
- Obtuse Angled Triangles
- Divisor Square Sum
- Combined Volume of Cuboids
- Flea Circus
- Totient Chains
- Crack-free Walls
- Investigating the primality of numbers of the form 2n2-1
- Balanced Numbers
- Perfect right-angled triangles
- Skew-cost coding
- Heighway Dragon
- Alexandrian Integers
- Sphere Packing
- Almost right-angled triangles I
- Almost right-angled triangles II
- Tribonacci non-divisors
- A Scoop of Blancmange
- The Chase
- Minkowski Sums
- Four Representations using Squares
- Fibonacci Words
- The prime factorisation of binomial coefficients
- The Race
- Lattice points on a circle
- Semidivisible numbers
- An Arithmetic Geometric sequence
- Luxury Hampers
- Tours on a 4 x n playing board
- Infinite string tour
- Twenty-two Foolish Primes
- Top Dice
- Perfection Quotients
- Odd Triplets
- Resilience
- Sliders
- Coresilience
- Tangents to an ellipse
- Squares under a hyperbola
- Numbers for which Euler’s totient function equals 13!
- Prime Subset Sums
- 250250
- Cardano Triplets
- Convex Holes
- Tidying up
- Sums of Digit Factorials
- Rounded Square Roots
- Tatami-Free Rooms
- Angular Bisectors
- A lagged Fibonacci sequence
- Reachable Numbers
- Stone Game
- Pivotal Square Sums
- Mountain Range
- An engineers' dream come true
- Triangle Centres
- Binary Circles
- Pseudo Square Root
- Billionaire
- Counting numbers with at least four distinct prime factors less than 100
- Polynomials with at least one integer root
- Cutting Squares
- Modular Cubes, part 1
- Modular Cubes, part 2
- Sum of Squares
- Divisibility Multipliers
- Balanced Sculptures
- Primitive Triangles
- A Modified Collatz sequence
- Linear Combinations of Semiprimes
- Triangles with integral sides and an integral angle
- Ant and seeds
- Pizza Toppings
- The Ackermann function
- Integer sided triangles for which the area/perimeter ratio is integral
- Steady Squares
- Pythagorean odds
- Scoring probabilities
- Quadtree encoding (a simple compression algorithm)
- An enormous factorial
- Eulerian Cycles
- Digital Signature
- Panaitopol Primes
- Pythagorean Polygons
- Pseudo-Fortunate Numbers
- Sum of digits - experience #23
- Lenticular holes
- Angular Bisector and Tangent
- Zeckendorf Representation
- Selective Amnesia
- Three similar triangles
- Protein folding
- Nim
- Strong Achilles Numbers
- Multiples with small digits
- Primonacci
- Reflexive Position
- Paper-strip Game
- Chip Defects
- An amazing Prime-generating Automaton
- Integer Ladders
- Nim Square
- Biclinic Integral Quadrilaterals
- Cyclic paths on Sierpiński graphs
- Sliding game
- The Mouse on the Moon
- Digital root clocks
- Numbers in decimal expansions
- Firecracker
- 2011 nines
- Bounded Sequences
- Factorials divisible by a huge integer
- Swapping Counters
- Binomial coefficients divisible by 10
- Bitwise-OR operations on random integers
- Building a tower
- Stone Game II
- Modulo Summations
- Rooms of Doom
- Lowest-cost Search
- Prime Frog
- Euler's Number
- Cross flips
- Spherical triangles
- Special partitions
- Spilling the beans
- Gathering the beans
- Maximix Arrangements
- Totient Stairstep Sequences
- Cutting Rectangular Grid Paper
- Peredur fab Efrawg
- Crazy Function
- Golomb's self-describing sequence
- The totient of a square is a cube
- Fractional Sequences
- Silver dollar game
- Matrix Sum
- Strong Repunits
- Largest integer divisible by two primes
- Sum of a square and a cube
- Langton's ant
- Constraining the least greatest and the greatest least
- Hexagonal orchards
- Blood tests
- Risky moon
- Distances in a bee's honeycomb
- Maximal coprime subset
- Largest roots of cubic polynomials
- Prime generating integers
- Cyclic numbers
- Hilbert's New Hotel
- Scary Sphere
- Subsequence of Thue-Morse sequence
- Squarefree factors
- Bézier Curves
- Comfortable distance
- A huge binomial coefficient
- Stone Game III
- Bozo sort
- A Kempner-like series
- Badugi
- Geometric triangles
- Licence plates
- Pencils of rays
- Circumscribed Circles
- Maximum Integer Partition Product
- Minimum of subsequences
- Nontransitive sets of dice
- Sum of digits, experience 13
- Triangle Triples
- Least common multiple count
- Amazing Mazes!
- (prime-k) factorial
- Generating polygons
- Divisibility comparison between factorials
- Rudin-Shapiro sequence
- Ellipses inside triangles
- Maximum length of an antichain
- Harshad Numbers
- Distinct Lines
- Platonic Dice
- Triangles with non rational sides and integral area
- Hopping Game
- Enmeshed unit circle
- Migrating ants
- Eating pie
- Pythagorean tree
- Weak Goodstein sequence
- Triangle on parabola
- Cutting rope
- Squarefree Fibonacci Numbers
- Fibonacci tree game
- Sum of squares of divisors
- Integer-valued polynomials
- Lattice points enclosed by parabola and line
- Crisscross Ellipses
- A rectangular tiling
- Guessing Game
- Idempotents
- Admissible paths through a grid
- Nim Extreme
- Circle and tangent line
- Uphill paths
- Gnomon numbering
- One-child Numbers
- Kaprekar constant
- Titanic sets
- A frog's trip
- Reciprocal cycles II
- Factorisation triples
- Look and say sequence
- 2x2 positive integer matrix
- Prime factors of n15+1
- Sequence of points on a hyperbola
- Consecutive die throws
- Kakuro
- Prime connection
- Box-ball system
- n-sequences
- Necklace of circles
- Sum of squares of unitary divisors
- Range flips
- Square Space Silo
- Totient sum
- Steps in Euclid's algorithm
- Rigid graphs
- Polynomials of Fibonacci numbers
- Unfair wager
- Fibonacci primitive roots
- Integer part of polynomial equation's solutions
- Sum of sum of divisors
- GCD and Tiling
- The inverse summation of coprime couples
- Eleven-free integers
- GCD sequence
- The Roundtable Lottery
- Retractions A
- Retractions B
- Retractions C
- Average least common multiple
- Chocolate covered candy
- Hypocycloid and Lattice points
- Modular inverses
- Long Products
- Lattice Quadrilaterals
- Diophantine reciprocals III
- Powers With Trailing Digits
- Triangles containing the origin II
- A polynomial modulo the square of a prime
- Permutations of Project
- Flipping game
- An ant on the move
- Almost Pi
- Permutation of 3-smooth numbers
- A weird recurrence relation
- Möbius function and intervals
- Polar polygons
- Distinct terms in a multiplication table
- Superinteger
- Smooth divisors of binomial coefficients
- Empty chairs
- Super Ramvok
- Triangle inscribed in ellipse
- Comfortable Distance II
- Phigital number base
- Last digits of divisors
- Music festival
- Circle Packing II
- Number Sequence Game
- Mixtures
- Roots on the Rise
- The Last Question
- Chef Showdown
- The incenter of a triangle
- Repeated permutation
- Arithmetic Derivative
- Maximum number of divisors
- Palindrome-containing strings
- Sums of power sums
- Unbalanced Nim
- Common factors between two sequences
- Jumping frog
- Double pandigital number divisible by 11
- Exploding sequence
- Under The Rainbow
- Collatz prefix families
- Writing n as the product of k distinct positive integers
- Incenter and circumcenter of triangle
- Drunken Tower of Hanoi
- Remainder of polynomial division
- St. Petersburg Lottery
- Problem 500!!!