Sometimes a piece of mathematics can be so neat and elegant, it makes you want to shout "eureka!" even if you haven't produced it yourself. One of our favourite examples of this is the art gallery problem.

The Guggenheim Museum in Bilbao: hard to supervise. Image: MykReeve.

Suppose you have an art gallery containing priceless paintings and sculptures. You would like it to be supervised by security guards, and you want to employ enough of them so that at any one time the guards can between them oversee the whole gallery. How many guards will you need?

Think about this for a while (go on, it's Sunday) and once you've had enough, read about the answer and its proof here. It's pure genius!

This article was inspired by Wild Maths, which encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. The site is aimed at 7 to 16 year-olds, but open to all. It provides games, investigations, stories and spaces to explore, where discoveries are to be made. Some have starting points, some a big question and others offer you a free space to investigate.

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