The Tower of Hanoi

This puzzle was invented in 1883 by the French mathematician Edouard Lucas.
The aim of the puzzle is to mover the tower to another rod. here are the rules:

• You may only move one disc at a time
• You may not place a larger disc on top of a smaller disc

1. What is the fewest number of moves it would take to solve the puzzle?

How I worked it out is:

Since there are 4 levels on the tower, it will take 15 moves to move the whole tower to another rod.

This is how I worked it out:

Key:

Forth level

Third level

Second level

First level

Tower of Hanoi by hannah from Room16 Parkvale on Vimeo.

    2.  What is the fewest number of moves it would take to solve the puzzle if there were 9 discs in             the tower?

How I worked it out is:
I worked out the pattern. Every time you add a level to the tower it makes you have to use more moves to get them back into order and on another rod.
Pattern is:  Each time you add a level the tower, to get the final amount of moves you have to double the previous amount of moves then add one more move to the answer.

This is how I worked out how many moves it would take:

• 1 level - 1 move
• 2 level - 3 moves
• 3 level - 7 moves
• 4 level - 15 moves
• 5 level - 31 moves
• 6 level - 63 moves
• 7 level - 127 moves
• 8 level - 255 moves
• 9 level - 511 moves

So it will take 511 moves to get the whole tower to another rod if there were 9 levels on it.