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## Project Euler 65: Convergents of e – SOLVED

Project Euler 65 Problem Statement The first ten terms in the sequence of convergents for e are: 2, 3, 8/3, 11/4, 19/7, 87/32, 106/39, 193/71, 1264/465, 1457/536, … The sum of digits in the numerator of the 10th convergent is 1+4+5+7=17. Find the sum of digits...

## Project Euler 3: Largest prime factor – SOLVED

Project Euler 3 Problem Statement The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ? Solution This problem is solved without using arrays or a giant list of prime numbers. Instead, we generate prospective...

## Project Euler 8: Largest product in a series – SOLVED

Project Euler 8 Problem Statement The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832. 73167176531330624919225119674426574742355349194934699893520312774506326239578318016984… Find the greatest product of 13...

## Project Euler 13: Large sum – SOLVED

Project Euler 16 Problem Statement Work out the first ten digits of the sum of the following one-hundred 50-digit numbers. 3710728753390210279879799822083759024651013574025046376937677490009712648124896970078050417018260538 … {data continues} Solution Summing a...

## Project Euler 2: Even Fibonacci numbers – SOLVED

Project Euler 2 Problem Statement Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, … Find the sum of all the even-valued terms in the...

## Project Euler 6: Sum square difference – SOLVED

Project Euler 16 Problem Statement The sum of the squares of the first ten natural numbers is 1² + 2² + … + 10² = 385. The square of the sum of the first ten natural numbers is (1 + 2 + … + 10)² = 55² = 3025. Hence the difference between the sum of the...