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'The Perforated Cube' printed from http://nrich.maths.org/

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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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