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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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A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?

Packing Small Boxes

Age 11 to 14 Short Challenge Level:

A large box measures 1.7 m by 1.2 m by 1.5 m.

It is to be packed with smaller boxes each measuring 15 cm by 20 cm by 20 cm.

What is the greatest number of small boxes that can be fitted into the larger box, assuming that they are all placed in the same orientation?



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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