Project Euler

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 41
• Problem 42
• Problem 43
• Problem 44
• Problem 45
• Problem 46
• Problem 47
• Problem 48
• Problem 49
• Problem 50

• 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 110
• Problem 111
• Problem 112
• Problem 113
• Problem 114
• Problem 115
• Problem 116
• Problem 117
• Problem 118
• Problem 119

• Problem 150
• 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

• Problem 190
• Problem 191
• Problem 192
• Problem 193
• Problem 194
• Problem 195
• Problem 196
• Problem 197
• Problem 198
• Problem 199

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

• Problem 301
• Problem 310
• Problem 312
• Problem 319
• Problem 323
• Problem 328
• Problem 334
• Problem 337
• Problem 345
• Problem 346
• Problem 355
• Problem 356
• Problem 364
• Problem 367
• Problem 373
• Problem 378
• Problem 382
• Problem 389
• Problem 391

Grid 5: Problems 500-599

• Problem 400
• 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