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Snail's Pace

Age 14 to 16 Short Challenge Level:

A snail is at one corner of the top face of a cube with side length 1m.

The snail can crawl at a speed of 1m per hour.

What proportion of the cube's surface is made up of points which the snail could reach within one hour?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.