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Which is a better fit, a square peg in a round hole or a round peg in a square hole?

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If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

Washing Elephants

Age 11 to 14 Short Challenge Level:

Mary and Nigel look after elephants in a zoo.

Mary takes 50 minutes to wash an elephant and Nigel takes 40 minutes to wash an elephant.

If they wash an elephant together, how long will it take them?




This problem is taken from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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