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Difficulty: Tricky

Sian is making a big, shiny cube in Minecraft. It will be 10 blocks wide, 10 blocks deep and 10 blocks high. The outer layer of blocks will be made of gold. Everything inside the cube will be made of obsidian.

Will Sian need more gold blocks, or more obsidian ones?

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

Brainteaser hint

Sian will need 10 x 10 x 10 = 1000 blocks

Brainteaser answer

As mentioned in the hint, Sian will need 10 x 10 x 10 = 1000 blocks. If more than half the blocks (more than 500 blocks) are obsidian, there must be more obsidian than gold.

Imagine taking the gold outer layer off the cube. Inside, there will be an 8 x 8 x 8 cube made of obsidian. To make this cube, Sian needs 8 x 8 x 8 = 512 cubes of obsidian. Since that’s more than 500 cubes, Sian will need more obsidian than gold.

We can also calculate the number of gold cubes. One way breaks down the gold into different bits.

• There are 8 gold cubes in the corners.
• Along each of the 12 edges there are 8 more gold cubes, 12 x 8 = 96.
• The remaining gold cubes are in the middle of each face. These squares are 8 x 8 and there are 6 of them. 8 x 8 x 6 = 384

Together, there are 8 + 96 + 384 = 488 gold cubes! Since that’s less than 500 cubes, Sian will need more obsidian than gold.

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