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Well done to all of you who sent in solutions to this problem - there are too many to mention you all, I'm afraid. Not so many of you answered both parts of the question, though! Mrs Alford's Maths Challenge Group at West Lodge Middle School, Mathew and Sam from Woodfall Primary and Linden from Comberton Village College explained their thinking clearly. West Lodge pupils say:40 cubes were not drilled.
Sakib from Swanlea School sent us a picture which really helps the visualisation:
William from St Patrick's School found a solution to the second part of the problem too:If you were to drill through the centre 4 cubes (that are also 4 cubes deep) then 4 cubes x 4 cubes = 16.
Another William, from Dane Court Grammar, agreed with this.