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Project Euler 1: Multiples of 3 and 5 – SOLVED

Project Euler 1 Problem Statement If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000. Solution Obvious solution This can be...

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 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 4: Largest palindrome product – SOLVED

Project Euler 4 Problem Statement A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99. Find the largest palindrome made from the product of two 3-digit numbers. Solution We can quickly...

Project Euler 5: Smallest multiple – SOLVED

Project Euler 5 Problem Statement 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smallest number that is evenly divisible by all of the numbers from 1 to 20? Solution Euclid’s algorithm 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...