# Towers of Hanoi Quiz Puzzle

The Towers of Hanoi is a well-known puzzle, but we have a bit of a twist on the old favourite.

In the puzzle there are five discs of different sizes that have a hole in the middle, and three pegs. At the start of the puzzle the five discs are on peg one, and each disc is on a disc that is bigger than it. That is, the biggest disc is at the bottom, the second biggest next, up to the smallest disc on top.

The challenge is to move all five discs to peg two. However, you can only move one disc at a time, and you cannot put a disc on top of a disc that is smaller than it. You can place a disc on an empty peg.

If you have not seen the puzzle before it is fun to try to solve it. Use five coins of different sizes as a makeshift version.

Solving the puzzle does take a lot of moves; probably more than you first expect.

So the first part of the puzzle - how many moves does the five-disc puzzle take?

And the second part - can you produce a formula for the number of moves with any number of discs?