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Colour in the Square

Age 7 to 16 Challenge Level:

Colour in the Square

Can you put the $25$ coloured tiles into the $5\times 5$ square below so that no column, no row and no diagonal line have the same colour in them?

Use the interactivity below to try out your ideas.

Full screen version

A practical version of this activity is included in one of the Brain Buster Maths Boxes which contains hands-on challenges developed by members of NRICH and produced by BEAM. For more details and ordering information, please scroll down this page .

Why do this problem?

This problem is one that requires working systematically. It is a good activity for promoting discussion between learners working together and also for giving encouragement to those whose spatial ability is better than their numerical achievements.

Key questions

Which row and which column have none of that colour in them?
Have you checked the diagonals as well as the rows and columns?

Possible extension

Learners could try other-sized squares such as $4\times 4$ and $6\times 6$. With some squares it is possible to place one colour correctly but no more. Of which sized squares is this true?

Possible support

You could suggest starting with just one colour, then fitting in the other colours, one at a time.