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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 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...

Project Euler 56: a^b maximum digit sum – SOLVED

Project Euler 56 Problem Statement Considering natural numbers of the form, ab, where a, b < 100, what is the maximum digit sum for all the powers? For example 187 is 612220032 and the digit sum for this power is 18. Solution Python natively supports...

Project Euler 20: Factorial digit sum – SOLVED

Project Euler 20 Problem Statement n! means n × (n − 1) × … × 3 × 2 × 1 Find the digit sum in the number 100! Solution Python natively supports arbitrary-precision integers and arithmetic with as many digits as necessary to perform a calculation.  100! requires...