Currently attending college in the Northeast of England.

Molly Ireland

Research Assistant, Durham University Maths Department.

In one nursery, a game that the children can play is stacking a set of cogs on top of one another. These cogs are different shapes, colours and sizes, which means this could be done in a sequence or pattern.

As shown in the image below, one child decided to stack the cogs from biggest to smallest. Some of the cogs had different-shaped teeth, making it hard to compare the sizes of the cogs. Here, the child could develop a rule to determine which cog would be classed as the largest.

A child stacking differently sized cogs onto a threaded pole, almost in size order

A famous mathematical game that involves stacking cogs is the Tower of Hanoi. It involves moving a tower of objects ordered by size from one peg to another. The disks (like our cogs in this case) all start by being organised in size order on one peg. There are three pegs in total, and the goal is to move the tower to the third peg. To do this, you can move one disk at a time, and you can only place a disk on top of a larger disk. An example of how to do this with three disks is shown below.

A play thorugh of the Tower of Hanoi game with three disks.

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