## The Vault: Powers of two

My new book of maths puzzles is on its way! It’s packed full of interesting problems to sink your teeth into. I’ll post an update as the launch approaches.

In the meantime, here is a fantastic problem from the USA:

It is given that $2^{2004}$ is a 604-digit number beginning with a 1. How many of the numbers $2^0, 2^1, 2^2, 2^3, ..., 2^{2003}$ begin with a 4?