# Project Euler

### From charlesreid1

## Contents

## Round 1: Problems 1-20

Project Euler/1 - Multiples of 3 and 5 - printing out all multiples of 3 and 5.

Project Euler/2 - Even Fibonacci - summing the Fibonacci numbers that are even and less than 4 million

Project Euler/3 - Largest Prime Factor - Largest prime factor of a given 12-digit number

Project Euler/4 - Largest Palindrome Product - Largest palindrome product (extracting substrings and sorting)

Project Euler/5 - LCM - Least common multiple of all the integers from 1 to 20

Project Euler/6 - SoS - Sum of squares and squares of sums

Project Euler/7 - Ten Thousand Primes - Find the 10,001st prime.

Project Euler/8 - Adjacent Digits - Largest product formed by 13 adjacent digits.

Project Euler/9 - Pythagorean Triplet Sum - Finding a Pythagorean triplet with a specified sum.

Project Euler/10 Sum of Primes - Sum of all primes below 2 million.

Project Euler/11 Greatest Product in Grid - Finding the greatest product of 4 numbers on a grid.

Project Euler/12 Highly Factorable Triangular Numbers - Finding highly factorable triangular numbers

Project Euler/13 Sum of Big Numbers - Work out the first 10 digits of a sum of 100 50-digit numbers

Project Euler/14 Longest Collatz Sequence - Finding the longest Collatz sequence for starting integers under 1 million

Project Euler/15 Lattice Paths - Finding the number of variations on a route through a lattice.

Project Euler/16 Summing the Digits - summing up the digits of a large power of 2, 2**1000

Project Euler/17 Number Spelling - spelling out all the numbers from one to a thousand

Project Euler/18 Shortest Path through a Triangle - find the path through a triangle of numbers that leads to the smallest sum

Project Euler/19 Counting Sundays

Project Euler/20 Sum of digits of 100! - straightforward use of BigInteger.

## Round 2: Problems 50-70

Project Euler/51 Prime Replacement - Finding the number of primes that can be formed by replacing particular digits of a number

Project Euler/52 Permuted Multiples - Find a number whose multiples 2x, 3x, 4x, 5x ad 6x are permutations of one another.

Project Euler/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.

Project Euler/62 Cyclic permutations of cubes - find cubes that permute to other cubes.

Project Euler/63 Powerful digit counts - finding n-digit numbers that are n-th powers

**Problems 64-66: Continued Fractions**

Project Euler/64 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.

Project Euler/65 Convergents of e - computing the 100th convergent (rational representation of continued fraction) for e and the square root of 2.

Project Euler/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.

Project Euler/67 Maximum path sum - a retake on Project Euler/18 with a larger triangle for which a brute force solution technique is impossible.

## Round 3: Problems 100-110

Project Euler/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.

Project Euler/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/Problem 102 - Triangles Containing Origin - given 3 endpoints, determine if a triangle contains the origin.

## Round 4: Problems 500-510

Project Euler/500 Smallest Number with 2n Factors - Finding the smallest number with 2^n divisors

Project Euler/501 Eight Divisors - Finding numbers with exactly 8 divisors, less than 1 trillion

Project Euler/502 Castles - finding the maximum number of castles that can be formed on extremely large grids

## Round 5: problems 170-180

Project Euler/172 Few Repeated Digits - how many 18 digit numbers have no digit occurring more than 3 times in n?

Project Euler
Problem 1
Problem 11
Problem 51
Problem 100
Problem 500
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