Project Euler: Difference between revisions

Revision as of 21:11, 17 June 2026

Grid 0: Problems 1-99

Problem 1- Multiples of 3 and 5 - printing out all multiples of 3 and 5.
Problem 2 - Even Fibonacci - summing the Fibonacci numbers that are even and less than 4 million
Problem 3 - Largest Prime Factor - Largest prime factor of a given 12-digit number
Problem 4 - Largest Palindrome Product - Largest palindrome product (extracting substrings and sorting)
Problem 5 - LCM - Least common multiple of all the integers from 1 to 20
Problem 6 - SoS - Sum of squares and squares of sums
Problem 7 - Ten Thousand Primes - Find the 10,001st prime.
Problem 8 - Adjacent Digits - Largest product formed by 13 adjacent digits.
Problem 9 - Pythagorean Triplet Sum - Finding a Pythagorean triplet with a specified sum.
Problem 10 Sum of Primes - Sum of all primes below 2 million.

Problem 11 - Greatest Product in Grid - Finding the greatest product of 4 numbers on a grid.
Problem 12 - Highly Factorable Triangular Numbers - Finding highly factorable triangular numbers
Problem 13 - Sum of Big Numbers - Work out the first 10 digits of a sum of 100 50-digit numbers
Problem 14 - Longest Collatz Sequence - Finding the longest Collatz sequence for starting integers under 1 million
Problem 15 - Lattice Paths - Finding the number of variations on a route through a lattice.
Problem 16 - Summing the Digits - summing up the digits of a large power of 2, 2**1000
Problem 17 - Number Spelling - spelling out all the numbers from one to a thousand
Problem 18 - Shortest Path through a Triangle - find the path through a triangle of numbers that leads to the smallest sum
Problem 19 - Counting Sundays
Problem 20 - Sum of digits of 100! - straightforward use of BigInteger.

Problem 27 - Quadratic Formula to Generate Primes
Problem 28 - Number Spiral Diagonals
Problem 29 - Distinct Terms Generated by Powers
Problem 30 - Sum of Fifth Power of Digits

Problem 31 - Polya - Change for a Dollar
Problem 32 - Pandigital Products (A X B = C covering all 9 digits)
Problem 33
Problem 40

Problem 51- Prime Replacement - Finding the number of primes that can be formed by replacing particular digits of a number
Problem 52- Permuted Multiples - Find a number whose multiples 2x, 3x, 4x, 5x ad 6x are permutations of one another.
Problem 53 - Number of Combinations Over 1M - Find how many different n choose r values are greater than 1 million for n between 1 and 100.
Problem 54 - Comparing poker hands to determine a winner
Problem 55
Problem 56
Problem 57
Problem 58 - Counting how many composite numbers have exactly 8 factors
Problem 59 - Decrypting 3-letter secret key (Vigenere cipher)
Problem 60 - Prime pair sets - finding five primes such that any prime pair can be concatenated to form a new prime

Problem 61 - Six cyclic 4-digit numbers, each of which are polygonal numbers (triangle, square, pentagonal, hexagonal, heptagonal, octagonal)
Problem 62 - Cyclic permutations of cubes - find cubes that permute to other cubes.
Problem 63 - Powerful digit counts - finding n-digit numbers that are n-th powers
Problem 64 - Continued Fractions - Odd period square roots - finding the continued fraction representation of an odd number, and determining if it has an odd period. First 1,000 numbers, so these sequences get LONG.
Problem 65 - Convergents of e - computing the 100th convergent (rational representation of continued fraction) for e and the square root of 2.
Problem 66 - Diophantine equation - a nice problem involving quadratic Diphantine equations called Pell equations. These equations can be solved using the technique of continued fraction representations. It is much easier to solve this problem, then 64 and 65, rather than the other way around.
Problem 67 - Maximum path sum - a retake on Project Euler/18 with a larger triangle for which a brute force solution technique is impossible.
Problem 68
Problem 69
Problem 70

Grid 1: Problems 100-199

Problem 100 - Combinations of Red and Blue Discs - find arrangements of blue and red discs that lead to a probability of exactly 50% that a blue disc is removed, two times in a row.
Problem 101 - Bad Optimal Polynomials - Lagrangian polynomial interpolation for a sequence of numbers, interpolation of an optimal N-1 polynomial given N points of data.
Problem 102 - Triangles Containing Origin - given 3 endpoints, determine if a triangle contains the origin.
Problem 103 - Special Subset Sums: Optimum - finding the optimum special sum set with n=7.
Problem 104 - Pandigital Fibonacci Ends - finding Fibonacci numbers with pandigital beginnings and endings.
Problem 105 - Special Subset Sums: Testing - testing sets for the special sum property.
Problem 106 - Special Subset Sums: Meta-testing - counting subset pairs that need to be tested.
Problem 107 - Minimal Network - finding the minimal network connecting all vertices (minimum spanning tree).
Problem 108 - Diophantine Reciprocals I - solving 1/x + 1/y = 1/n for distinct solutions.
Problem 109 - Darts - counting the number of distinct ways to check out in darts with a score less than 100.

Problem 110 - Diophantine Reciprocals II - finding the smallest n with over 4 million solutions to 1/x + 1/y = 1/n.
Problem 111 - Primes with Runs - finding primes with maximum runs of repeated digits.
Problem 112 - Bouncy Numbers - counting numbers whose digits are neither increasing nor decreasing.
Problem 113 - Non-bouncy Numbers - counting numbers below a googol that are not bouncy.
Problem 114 - Counting Block Combinations I - counting ways to fill a row with red and grey blocks.
Problem 115 - Counting Block Combinations II - finding the minimum row length for over 1 million fill combinations.
Problem 116 - Red, Green or Blue Tiles - counting ways to replace tiles with colored blocks.
Problem 117 - Red, Green, and Blue Tiles - counting ways to place colored tiles of various lengths.
Problem 118 - Pandigital Prime Sets - partitioning the digits 1-9 into sets of prime numbers.
Problem 119 - Digit Power Sum - finding numbers equal to the sum of their digits raised to some power.

Problem 120 - Square Remainders - sum of maximum remainders when (a−1)^n + (a+1)^n is divided by a^2.
Problem 121 - Disc Game Prize Fund - finding max prize fund for a disc game with changing probabilities.
Problem 122 - Efficient Exponentiation - computing n^15 using minimal multiplications (addition chains).
Problem 123 - Prime Square Remainders - finding the prime where the maximum remainder exceeds 10^10.
Problem 124 - Ordered Radicals - finding the k-th element when numbers are sorted by their radical (product of prime factors).
Problem 125 - Palindromic Sums - sums of consecutive squares that are palindromic numbers.
Problem 126 - Cuboid Layers - counting the number of cubes needed to cover visible faces of cuboids in successive layers.
Problem 127 - abc-hits - counting triples where rad(abc) < c and a and b are coprime.
Problem 128 - Hexagonal Tile Differences - finding tiles in a hexagonal spiral where all neighbors have prime differences.
Problem 129 - Repunit Divisibility - finding the least n such that a repunit R(n) is divisible by a given number.
Problem 130 - Composites with Prime Repunit Property - composite numbers where n divides the repunit R(n−1).

Problem 131 - Prime Cube Partnership - primes p for which n^3 + n^2·p is a perfect cube.
Problem 132 - Large Repunit Factors - sum of the first forty prime factors of R(10^9).
Problem 133 - Repunit Nonfactors - primes that will never divide any repunit R(10^n).
Problem 134 - Prime Pair Connection - connecting consecutive primes p1, p2 to form a number divisible by p2.
Problem 135 - Same Differences - solving x^2 − y^2 − z^2 = n where x, y, z form an arithmetic progression.
Problem 136 - Singleton Difference - finding n with exactly one solution to x^2 − y^2 − z^2 = n.
Problem 137 - Fibonacci Golden Nuggets - Fibonacci numbers appearing as solutions to a Pell-type Diophantine equation.
Problem 138 - Special Isosceles Triangles - isosceles triangles with integer height and half-base differing by 1.
Problem 139 - Pythagorean Tiles - Pythagorean triangles that allow tiling of a square of side equal to the hypotenuse.
Problem 140 - Modified Fibonacci Golden Nuggets - golden nuggets from a modified Fibonacci sequence.

Problem 141 - Square Progressive Numbers - perfect squares that are also progressive (geometric progression of digits).
Problem 142 - Perfect Square Collection - finding x+y+z where x>y>z>0, all pairwise sums/differences are squares.
Problem 143 - Torricelli Triangles - triangles whose Torricelli point has integer distances to the vertices.
Problem 144 - Laser Beam Reflections - reflecting a laser beam inside an elliptical mirror until it exits.
Problem 145 - Reversible Numbers - counting numbers n below 1 billion where n + reverse(n) has all odd digits.
Problem 146 - Investigating a Prime Pattern - finding n where n^2+1, n^2+3, n^2+7, n^2+9, n^2+13, n^2+27 are consecutive primes.
Problem 147 - Rectangles in Cross-hatched Grids - counting all rectangles in a cross-hatched rectangular grid.
Problem 148 - Exploring Pascal's Triangle - counting entries in the first billion rows of Pascal's triangle not divisible by 7.
Problem 149 - Maximum-sum Subsequence - finding the maximum sum of adjacent subsequences in a generated 2000×2000 array.
Problem 150 - Sub-triangle Sums - finding the minimum-sum sub-triangle in a triangular array of 1000 rows.

Problem 151
Problem 152
Problem 153
Problem 154
Problem 155
Problem 156
Problem 157
Problem 158 - Strings of various lengths, with exactly one character lexicographically out of sorts
Problem 159

Problem 170
Problem 171
Problem 172 - Few Repeated Digits - how many 18 digit numbers have no digit occurring more than 3 times in n?
Problem 173
Problem 174
Problem 175
Problem 176
Problem 177
Problem 178
Problem 179

Grid 2: Problems 200-299

Problem 227
Problem 254 - Maximum Source of Sums of Digits of Sums of Digits of Sums of Factorial Digit Sums

Grid 3: Problems 300-399

Grid 4: Problems 400-499

Problem 400

Grid 5: Problems 500-599

Problem 500 - Smallest Number with 2n Factors - Finding the smallest number with 2^n divisors
Problem 501 - Eight Divisors - Finding numbers with exactly 8 divisors, less than 1 trillion
Problem 502 - Castles - finding the maximum number of castles that can be formed on extremely large grids

Grid 9: Problems 900-999

Problem 932

@@ Line 71: / Line 71: @@
 * [[Project Euler/101|Problem 101]] - Bad Optimal Polynomials - Lagrangian polynomial interpolation for a sequence of numbers, interpolation of an optimal N-1 polynomial given N points of data.
 * [[Project Euler/102|Problem 102]] - Triangles Containing Origin - given 3 endpoints, determine if a triangle contains the origin.
+* [[Project Euler/103|Problem 103]] - Special Subset Sums: Optimum - finding the optimum special sum set with n=7.
+* [[Project Euler/104|Problem 104]] - Pandigital Fibonacci Ends - finding Fibonacci numbers with pandigital beginnings and endings.
+* [[Project Euler/105|Problem 105]] - Special Subset Sums: Testing - testing sets for the special sum property.
+* [[Project Euler/106|Problem 106]] - Special Subset Sums: Meta-testing - counting subset pairs that need to be tested.
+* [[Project Euler/107|Problem 107]] - Minimal Network - finding the minimal network connecting all vertices (minimum spanning tree).
+* [[Project Euler/108|Problem 108]] - Diophantine Reciprocals I - solving 1/x + 1/y = 1/n for distinct solutions.
+* [[Project Euler/109|Problem 109]] - Darts - counting the number of distinct ways to check out in darts with a score less than 100.
-* [[Project Euler/110|Problem 110]]
+* [[Project Euler/110|Problem 110]] - Diophantine Reciprocals II - finding the smallest n with over 4 million solutions to 1/x + 1/y = 1/n.
-* [[Project Euler/111|Problem 111]]
+* [[Project Euler/111|Problem 111]] - Primes with Runs - finding primes with maximum runs of repeated digits.
-* [[Project Euler/112|Problem 112]]
+* [[Project Euler/112|Problem 112]] - Bouncy Numbers - counting numbers whose digits are neither increasing nor decreasing.
-* [[Project Euler/113|Problem 113]]
+* [[Project Euler/113|Problem 113]] - Non-bouncy Numbers - counting numbers below a googol that are not bouncy.
-* [[Project Euler/114|Problem 114]]
+* [[Project Euler/114|Problem 114]] - Counting Block Combinations I - counting ways to fill a row with red and grey blocks.
-* [[Project Euler/115|Problem 115]]
+* [[Project Euler/115|Problem 115]] - Counting Block Combinations II - finding the minimum row length for over 1 million fill combinations.
-* [[Project Euler/116|Problem 116]]
+* [[Project Euler/116|Problem 116]] - Red, Green or Blue Tiles - counting ways to replace tiles with colored blocks.
-* [[Project Euler/117|Problem 117]]
+* [[Project Euler/117|Problem 117]] - Red, Green, and Blue Tiles - counting ways to place colored tiles of various lengths.
-* [[Project Euler/118|Problem 118]]
+* [[Project Euler/118|Problem 118]] - Pandigital Prime Sets - partitioning the digits 1-9 into sets of prime numbers.
-* [[Project Euler/119|Problem 119]]
+* [[Project Euler/119|Problem 119]] - Digit Power Sum - finding numbers equal to the sum of their digits raised to some power.
+* [[Project Euler/120|Problem 120]] - Square Remainders - sum of maximum remainders when (a−1)^n + (a+1)^n is divided by a^2.
+* [[Project Euler/121|Problem 121]] - Disc Game Prize Fund - finding max prize fund for a disc game with changing probabilities.
+* [[Project Euler/122|Problem 122]] - Efficient Exponentiation - computing n^15 using minimal multiplications (addition chains).
+* [[Project Euler/123|Problem 123]] - Prime Square Remainders - finding the prime where the maximum remainder exceeds 10^10.
+* [[Project Euler/124|Problem 124]] - Ordered Radicals - finding the k-th element when numbers are sorted by their radical (product of prime factors).
+* [[Project Euler/125|Problem 125]] - Palindromic Sums - sums of consecutive squares that are palindromic numbers.
+* [[Project Euler/126|Problem 126]] - Cuboid Layers - counting the number of cubes needed to cover visible faces of cuboids in successive layers.
+* [[Project Euler/127|Problem 127]] - abc-hits - counting triples where rad(abc) < c and a and b are coprime.
+* [[Project Euler/128|Problem 128]] - Hexagonal Tile Differences - finding tiles in a hexagonal spiral where all neighbors have prime differences.
+* [[Project Euler/129|Problem 129]] - Repunit Divisibility - finding the least n such that a repunit R(n) is divisible by a given number.
+* [[Project Euler/130|Problem 130]] - Composites with Prime Repunit Property - composite numbers where n divides the repunit R(n−1).
+* [[Project Euler/131|Problem 131]] - Prime Cube Partnership - primes p for which n^3 + n^2·p is a perfect cube.
+* [[Project Euler/132|Problem 132]] - Large Repunit Factors - sum of the first forty prime factors of R(10^9).
+* [[Project Euler/133|Problem 133]] - Repunit Nonfactors - primes that will never divide any repunit R(10^n).
+* [[Project Euler/134|Problem 134]] - Prime Pair Connection - connecting consecutive primes p1, p2 to form a number divisible by p2.
+* [[Project Euler/135|Problem 135]] - Same Differences - solving x^2 − y^2 − z^2 = n where x, y, z form an arithmetic progression.
+* [[Project Euler/136|Problem 136]] - Singleton Difference - finding n with exactly one solution to x^2 − y^2 − z^2 = n.
+* [[Project Euler/137|Problem 137]] - Fibonacci Golden Nuggets - Fibonacci numbers appearing as solutions to a Pell-type Diophantine equation.
+* [[Project Euler/138|Problem 138]] - Special Isosceles Triangles - isosceles triangles with integer height and half-base differing by 1.
+* [[Project Euler/139|Problem 139]] - Pythagorean Tiles - Pythagorean triangles that allow tiling of a square of side equal to the hypotenuse.
+* [[Project Euler/140|Problem 140]] - Modified Fibonacci Golden Nuggets - golden nuggets from a modified Fibonacci sequence.
+* [[Project Euler/141|Problem 141]] - Square Progressive Numbers - perfect squares that are also progressive (geometric progression of digits).
+* [[Project Euler/142|Problem 142]] - Perfect Square Collection - finding x+y+z where x>y>z>0, all pairwise sums/differences are squares.
+* [[Project Euler/143|Problem 143]] - Torricelli Triangles - triangles whose Torricelli point has integer distances to the vertices.
+* [[Project Euler/144|Problem 144]] - Laser Beam Reflections - reflecting a laser beam inside an elliptical mirror until it exits.
+* [[Project Euler/145|Problem 145]] - Reversible Numbers - counting numbers n below 1 billion where n + reverse(n) has all odd digits.
+* [[Project Euler/146|Problem 146]] - Investigating a Prime Pattern - finding n where n^2+1, n^2+3, n^2+7, n^2+9, n^2+13, n^2+27 are consecutive primes.
+* [[Project Euler/147|Problem 147]] - Rectangles in Cross-hatched Grids - counting all rectangles in a cross-hatched rectangular grid.
+* [[Project Euler/148|Problem 148]] - Exploring Pascal's Triangle - counting entries in the first billion rows of Pascal's triangle not divisible by 7.
+* [[Project Euler/149|Problem 149]] - Maximum-sum Subsequence - finding the maximum sum of adjacent subsequences in a generated 2000×2000 array.
+* [[Project Euler/150|Problem 150]] - Sub-triangle Sums - finding the minimum-sum sub-triangle in a triangular array of 1000 rows.
-* [[Project Euler/150|Problem 150]]
 * [[Project Euler/151|Problem 151]]
 * [[Project Euler/152|Problem 152]]

Project Euler: Difference between revisions

From charlesreid1

Revision as of 21:11, 17 June 2026

Contents

Grid 0: Problems 1-99

Grid 1: Problems 100-199

Grid 2: Problems 200-299

Grid 3: Problems 300-399

Grid 4: Problems 400-499

Grid 5: Problems 500-599

Grid 9: Problems 900-999