Prison Cells

Prison Cells

There are seventy eight prisoners in a square cell block of twelve cells. There is one prisoner in one of the cells, two in another cell, three in another, four in another and so on up to twelve prisoners in one of the cells.

The clever prison warder made it easy to check if the prisoners were all there by arranging them so there were twenty five along each wall of the prison block. How did he do it?

 

(There's more than one solution - send yours in - it might be different to everyone else's!)

Why do this problem?

Possible approach

Key questions

What have we got to find out?

What do we know?

Possible extension

Children who find one solution quickly could be encouraged to find another one by rearranging some of the numbers in their own solution, rather than beginning afresh. In doing so they are beginning to generalise, an important mathematical skill. If you ask the children to record each solution on a separate piece of paper, then by moving and rearranging them they can see there are 'families' of solutions.

Possible support

Children who find this difficult could be given the grid with the corners filled in so that they start at a different place but end up with a complete solution, as everyone else.