A Leafy Tower of Hanoi

4 November 2010 · 2 comments

in Maths Outdoors

The Tower of Hanoi is a maths puzzle that is traditionally completed on rods with wooden discs. Teacher Tom recently blogged about The Evolution of the Tree Part Toys and this reminded me of this puzzle.

However I am not as organised as Tom and although I’ve been meaning to make up some wooden discs and mini blocks, I simply haven’t got around to it. Undeterred, 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 in forest litter with a stick. Alternatively, sticks, stones, cones or any other material to hand can be used to make the three squares.

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 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.

With three leaves, it takes seven moves to complete the puzzle. With four leaves, it takes fifteen moves. With five leaves it takes thirty-one moves. Can you work out the pattern? 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 links with the Friday’s Nature Table at The Magic Onions Blog.

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{ 2 comments… read them below or add one }

Fiona November 5, 2010 at 20:11

A brilliant idea, and a super original adaptation that would make this far more ‘fun’ for younger kids. Love the leaves!


Bending Birches November 6, 2010 at 04:32

oh, I am almost breathing a sigh of relief here…I have struggled with math my entire life (see a recent post on my blog about not passing my PRAXIS) I do vividly remember trying to solve a “tower of hanoi” while in a math for elem. teachers course during my undergrad years. I couldn’t get it…I couldn’t explain it…it couldn’t be explained to me. I dropped the course after some time, but had to return to it to graduate. The same teacher…the same math puzzles! the tower of Hanoi!
Imagine if it was presented to me like this…..thank you:)


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