The Tower of Hanoi is a maths puzzle that is traditionally completed on rods with wooden discs. Teacher Tom blogged about The Evolution of the Tree Part Toys and this reminded me of this puzzle, I have resorted to leaves which are abundant and colourful at this time of year. This is a handy solution especially for those who visit local woods for learning.

The first job is to create a “base”. This can be drawn on a patch of earth with a stick. Alternatively, sticks, stones, cones or any other material to hand can be used to make the three squares. I use a white sheet as I like the focus this brings to maths and other activities.

Next, find three leaves of different sizes. I’ve used different colours as well so it is easier to see which leaf is smaller or bigger than the others. These go in the left hand square.

The aim of the puzzle is to move all the leaves into another square so they end up in the same order with the largest leaf on the bottom and the smallest leaf on top. There are some rules to follow.

Firstly only one leaf may be moved at a time.

You may only move the top leaf on a pile. It must be moved to one of the other squares.

No larger leaf may be placed on top of a smaller leaf.

With just three leaves this puzzle is straightforward. The more leaves in your pile, the more challenging the problem becomes. Can you work out the smallest number of moves required?

With three leaves, it takes seven moves to complete the puzzle. What about if you use 4 leaves? It takes at least fifteen moves. With 5 leaves it takes 31 moves. Can you work out the pattern? What do you predict will be the number of moves if you have a pile of 6 leaves. Did you predict this correctly? For getting into the deep maths, have a look at the Wiki page.

Children can use leaves on the ground by themselves or in pairs. However using tyres or large blocks of different sizes, spaced further apart, turns this into a much larger group problem solver especially if the team is timed to see how quickly they can complete the puzzle.

All-in-all, it’s an absorbing challenge for children and adults alike. Enjoy!

This post is an update of one that first appeared in November 2010.

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