Colour in the Square
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Age
7 to 16
Challenge level
Problem
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.
Printable NRICH Roadshow resource.
Getting Started
Try starting with just one colour, then fill in a colour at a
time.
Student Solutions
Liam and Joanne from Moorfield Junior School sent us this solution:
We worked out that every new line we started had to have each colour two spaces away from the same colour on the line above.
Image
Do you agree with them? Did you find any of the other ways to solve this problem?
Teachers' Resources
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.