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Dolly’s cheese is covered in wax

Difficulty: Tricky
Dolly bought a special cheese. It comes in a square block that’s 5 centimetres wide, 5 centimetres deep and 5 centimetres tall. It’s also coated in wax on all sides. Without removing the wax, Dolly cuts the cheese into 1 centimetre cubes.

Can you work out how many cubes have wax on them?

Scroll down or click for a hint, or the answer!

Brainteaser hint

How many cubes does Dolly cut? Can you work out how many cubes don’t have wax on them?

Brainteaser answer

Dolly’s cheese block is 5 cubes wide, 5 cubes deep and 5 cubes high. So it will contain 5 x 5 x 5 = 125 cubes.

All the cubes on the outside of the cheese have wax on them. If we take them away, we’re left with a 3 x 3 x 3 shape, with 27 unwaxed cubes of cheese.

To work out how many have wax, we can use subtraction. 125 cubes – 27 unwaxed cubes = 98 waxed cubes!

For a different approach, we can break the cheese into different pieces.
• There are 8 cubes in the corners
• There are 12 edges, each with 3 cubes that aren’t corners, and 12 x 3 = 36
• There are 6 faces, and each has 9 cubes that aren’t corners or edges. 6 x 9 = 54
Adding it all together, we get 8 + 36 + 54 = 98 waxed cubes.

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