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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...

Project Euler 7: 10001st prime – SOLVED

Project Euler 7 Problem Statement By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the 10001st prime number? Solution This solution will solve both this problem and the HackerRank version of Project Euler 7....

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 9: Special Pythagorean triplet – SOLVED

Project Euler 9 Problem Statement A Pythagorean triplet is a set of three natural numbers, a ≤ b < c, for which, For example, . There exists exactly one Pythagorean triplet for which a + b + c = 1000.Find the product abc. Solution A Pythagorean triple consists of...

Project Euler 10: Summation of primes – SOLVED

Project Euler 10 Problem Statement The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. Solution Using our prime number sieve introduced in problem 7 this is easy to solve in less than 100ms with a couple lines of...