Key Stage 2 Maths
Different Coloured Objects Challenge
Neena has some coloured tiles.
She has three green tiles, three purple tiles and three orange tiles.
She arranges them in a 3x3 grid like this:
Neena has a rule: Tiles of the same colour can touch in the corner but not along the side.
This would not be a solution because the two purple tiles touch along their sides:
Find as many ways as you can that Neena could arrange her tiles into a 3x3 square where tiles of the same colour do not meet at an edge.
How will you know if you have found them all?
Helpful Hints
You could begin with a 2x2 grid and two colours like this to see how you might tackle this problem and how many different ways it works with two colours and a smaller grid.
You could record this using letters to represent the colours like this:
P O
O P
Now move on to the 3x3 grid and three of each colour.
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Going Further
What if you were to allow the sides to touch?
How many different 2x2 and 3x3 solutions would there be now?
What if you added a fourth colour, say a blue tile and you had a 4x4 grid and four of each colour?