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Multilink Cubes

If you had 36 cubes, what different cuboids could you make?

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The Big Cheese

Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?

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Making Boxes

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

More Christmas Boxes

Age 7 to 11 Challenge Level:

Start with a $10$ by $10$ grid.

If you cut out each corner square, it could be folded into an open-top box that had an $8$ by $8$ base and was $1$ square deep. That means that the box would be able to hold $64$ cubes.


What size square should you cut out of each corner to make the box that would hold the greatest number of unit cubes?

(Another way to ask this question is 'Which box has the greatest volume of space available?'.)