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'Sweets in a Box' printed from http://nrich.maths.org/

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Miss Hooley's class from Harmans Water Primary School worked on this problem for quite a time. First they had a few questions to help them clarify their thinking:

Can the sweets be different shapes or different sizes?

If the box is triangular and the sweets are triangles too, won't the different colours meet at the corners?

Once the children had made their decisions about the shapes and sizes of the sweets they came up with a solution that they would like to share. It is easier to follow the directions if you draw out a shape first and then colour as you go through the steps.

Craig and Roshan, from Harmans Water Primary School, provide this detailed explanation.

"We had to put 36 sweets in a box with no gaps and there has to be four different colours and 9 of each colour. We found out it works with nearly every shape, and there is a method to doing this with most shapes.

1. Draw 9 of the shape that you are trying out.

2. Draw one shape inside the other, until all 9 shapes are used.

3. Divide the larger shape into 4 equal parts.

You will now have 36 pieces.

hexagon

To colour the sweets, you need to take two of your coloured pencils each time.

4. Colour alternative sweets in one of the corners until you reach the centre of the large shape.

5. Next, take the remaining two colours and do the same on the next quarter of the larger shape, closest to the part that you have just worked on.

6. Take the colours you started with, and do the same in the next section or quarter of the larger shape. This will be below the one you have just coloured and opposite to the first quarter you coloured.

7. Finally, take the second set of two colours and colour alternate sweets in the last quarter of the large shape.

You will now have 9 sweets of each colour. The sweets are different sizes though

Is this is allowed? We have drawn a copy for you to look at.

Craig and Roshan say, "Tell us what you think".