Sunday Teaser 2648 – Painted Cubes
by Graham Smithers
I found some painted cubes whose sides were varying whole numbers of centimetres.
After choosing some of these cubes whose edges were consecutive integers, I cut them all into smaller cubes with edge lengths of one centimetre.
I found that half of the resulting cubes had no painted faces.
How many of the small cubes had no painted faces?
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