Key Stage 2 Maths

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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:

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Neena has a rule: Tiles of the same colour can touch in the corner but not along the side. 

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This would not be a solution because the two purple tiles touch along their sides:

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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.

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How will you know if you have found them all?

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Helpful Hints​

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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.

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You could record this using letters to represent the colours like this:

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P   O

O   P    

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Now move on to the 3x3 grid and three of each colour.