## 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.

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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.