Chequered Cuboid
A large cuboid is made from cubes of equal size. What fraction of the surface area of the large cuboid is black?
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![Chequered Cuboid Chequered Cuboid](/sites/default/files/styles/large/public/thumbnails/content-id-11676-Weekly%2525202016%252520-%25252050%252520Diagram.png?itok=FFJm_NLu)
What fraction of the surface area of the cuboid is coloured black?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
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![Chequered Cuboid Chequered Cuboid](/sites/default/files/styles/large/public/thumbnails/content-id-11676-Weekly%2525202016%252520-%25252050%252520Solution%2525201.png?itok=xcEaYqi8)
Image
![Chequered Cuboid Chequered Cuboid](/sites/default/files/styles/large/public/thumbnails/content-id-11676-Weekly%2525202016%252520-%25252050%252520Solution%2525202.png?itok=Hsu5A2k4)
Therefore, between the four faces there are $6 \times 4 = 24$ white squares and $6 \times 4 = 24$ black squares.
Therefore, overall there are $9+24=33$ white squares and $9+24=33$ black squares, so $\frac{1}{2}$ of the squares are coloured black.