Unsolved Problems (2)

My favourite unsolved problem is the Collatz Conjecture which is named after mathematician Lothar Collatz, who introduced the idea in 1937.

Start with any positive whole number. If the number is odd, multiply by 3 and add 1. If the number is even, divide by two. Apply the rule  to the resulting new number.

For example, if we start with 7, we get the following sequence:

7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1.

The conjecture states that whatever the starting number, you always end up with 1.

It’s been tested for starting values up to 100304170900795686912 but nobody so far has proved that it’s true for all positive whole numbers.