The Coin Pyramid

On page 82 of Diabolical Brainbenders is a challenge called "Coin Pyramids and the End of the World". It's based on the legend of the Tower of Hanoi which has an army of monks moving massive gold discs about. However we've adapted this game so that you can play it by yourself.
How To Play
You start with three crosses on a bit of paper.
On one cross you put a pile of different sized coins
or counters with the biggest on the bottom.
(You can use as many different coins as you like.
The puzzle is quite easy with three coins, but with
more coins it gets trickier!)
The idea is to move the whole pile from one cross to another but:

you can only move one coin at once
you must never put a larger coin on a smaller one.

Here's how to start with 3 coins.

If you've had trouble understanding how to do it,
you can see the puzzle actually being solved
in front of you on the screen below!

Choose how many coins you want to start with
(or "random" if you're feeling a bit crazy)
then click START to watch it work.
You can also choose how fast the "coins" move.

Number of coins

Speed

This groovy little programme
was invented by AMIN WONG
and we got it from
The JavaScript Source

THE SECRET TO THE MOVEMENTS!
Watch how the "1" coin moves.
Every other turn it moves from post A to B
then from B to C and then from C back to A.
After the "1" disc has moved each time, only one
other coin can make a legal move, and so it does.

HOW MANY MOVES DOES IT TAKE?
There is a simple formula depending on
the number of coins you start with.
Can you work it out?
If not then drag your mouse over the red box:

If "C" = number of coins, then moves = (2^C-1)

PARTY TIP: if you're having a particularily dull evening, why not invite some friends round for pizza and select "8" coins and set it going on the slowest speed and all sit round and watch?

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