Colour in the Square
Can you put the 25 coloured tiles into the 5 × 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
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.
The children in Chatsworth Class at Oak Tree Primary School in Mansfield, UK used the ideas in the above solution to find a different way of colouring the square:
We used the pattern of Down 1, across 2 to set the example. We then used this to find a new solution which is:
Down 1 and across 3.
Alice and Alfie in Chatsworth class have completed the work. Here is a photo to show our evidence.
This solution is very interesting - it actually follows the same rule as the solution above, where the colours are two spaces away, because going down 1 and right 3 is the same as going down 1 and left 2!
I wonder if there are any solutions that don't follow Liam and Joanne's rule, where the colours in each new line are always two spaces away?
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
Key questions
Have you checked the diagonals as well as the rows and columns?
Possible extension
Possible support
You could suggest starting with just one colour, then fitting in the other colours, one at a time.