Problem 14

Which starting number, under one million, produces the longest Collatz sequence?

Problem 13

Work out the first ten digits of the sum of the following one-hundred 50-digit numbers.

Problem 12

What is the value of the first triangle number to have over five hundred divisors?

Problem 11

What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?

Problem 10

Find the sum of all the primes below two million.

Problem 9

There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.

Problem 8

Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?

Problem 7

What is the 10001st prime number?

Problem 6

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

Problem 5

What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

Problem 4

Find the largest palindrome made from the product of two 3-digit numbers.

Problem 3

What is the largest prime factor of the number 600851475143 ?

Problem 2

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

Problem 1

Find the sum of all the multiples of 3 or 5 below 1000.