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Problem 82

Geometry Difficulty 1.0 Prove it UKMT Senior Kangaroo · United Kingdom · 2016

Andrew has two containers for carrying water. The containers are cubes without tops and have base areas of $4\,\text{dm}^2$ and $36\,\text{dm}^2$ respectively. Andrew has to completely fill the larger cube with pond water, which must be carried from the pond using the smaller cube. What is the smallest number of visits Andrew has to make to the pond with the smaller cube?

This one wants a proof. Work it on paper, then check yourself against the publisher's own solution, linked below. Be honest about it: the record is only any use to you if it is.

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.