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?