You have a single sheet of wood that measures 1m by 1.5m and is 3mm thick. You wish to make a single hollow box from this sheet. The external surface of the box must be a cube of the largest possible surface area with no holes or defects. You may only use six separate pieces of wood, each of which must have square or rectangular faces. You should assume that no wood is lost in the cuts, but cuts can only be at right-angles to the main surface of the wood, i.e. no mitres, dove tails, tabs or cutting the wood down to a smaller thickness.

What is the volume of wasted wood?

Please enter the answer in cubic centimetres to three decimal places.

Mathsbombe Competition 2018 is organised by the The Department of Mathematics at The University of Manchester.
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