Copyright © University of Cambridge. All rights reserved.

'Six in a Circle' printed from

Show menu

A class of $30$ children were numbered from $1$ to $30$. Here are some of the class:

Eight children numbered from 1 to 8

Their teacher set out a ring of $6$ chairs.

Child number $1$ sat on the first chair, child number $2$ on the second chair, child number $3$ on the third and so on going round the circle, up to child number $6$. The teacher then asked child number $7$ to stand behind child $1$, child $8$ to stand behind number $2$ etc. They continued this pattern until all the children were either sitting on a chair, or standing behind one.

How many people were standing behind each chair?
Who was standing behind child number $3$?
What would happen if there were only $4$ chairs?