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The Perforated Cube

Age 14 to 16
Challenge Level Yellow star
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A large cube made from 125 smaller cubes, 5 by 5 by 5, is 'perforated' by removing cubes.

A 125 cube sparsely made of small floating cubes

Any cube may be removed so imagine some uncoloured, transparent cubes propping up anything that needs it.

If a 'perforated cube' has the three views (projections) below, what is the most and the least cubes possible to make a shape that has these three projections ? In other words what could be the most and the least cubes left from the original 125 ?



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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.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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