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'The Games' Medals' printed from http://nrich.maths.org/

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Some children from the class are thinking about races because they are interested in the Olympics. Afzal, Bengy and Chrissy like the idea of getting medals. They know that there are Gold, Silver and Bronze medals.

Afzal says that if he won he'd get Gold and if Bengy then came second he'd get Silver and Chrissy would then get Bronze.

Chrissy says that's right but if she'd come first she would get the Gold and then when Bengy came second he'd get Silver again and Afzal would get Bronze.

Bengy has other ideas too.

 ideas

If the children found all the different ways in which they could be first, second and third, how many would they find?

If we think of Gold first and then Silver and lastly Bronze then so far we have:

Afzal, Bengy, Chrissy

Chrissy, Bengy, Afzal

and whatever Bengy's ideas are.

Which ways can you find?