Problem: In the 20 x 20 grid below, four numbers along a diagonal line have been marked. 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 49 49 99 40 17 81 18 57 60 87 17 40…

Problem: The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. Solution: 1. Brute-force approach: 2. Efficient approach (using the Sieve…

Problem: A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a2 + b2 = c2 For example, 32 + 42 = 9 + 16 = 25 = 52. There exists exactly one Pythagorean triplet…

Problem: Find the greatest product of five consecutive digits in the 1000-digit number. 73167176531330624919225119674426574742355349194934…

Problem: 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 10,001st prime number? Solution: 1. Brute-force approach: 2.…

Problem: 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…

Problem: 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 positive number that is evenly divisible by all…

Problem: A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 x 99. Find the largest palindrome made from the…