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Puzzle from Maths Jam Nottingham: Kathryn’s cube of cheese

At Maths Jam Nottingham January 2012, Kathryn brought this puzzle.

Kathryn has a cube made of cheese. Her question is simple: What is the smallest number of tetrahedra (not necessarily regular) that you can cut the cube into, leaving no cheese left over?

If you think you’ve solved this, see the solution page below for a follow on question.

For occasional puzzles from Nottingham Maths Jam meetings are tagged so you can search for “mathsjam” and find them.

It is important in problem solving that you have an honest attempt before reading a solution. Once someone has shown you the solution you are forever robbed of the chance to have that experience (in future you will half-remember the solution rather than reason it out) so it is important that you attempt this puzzle before reading the solution. If you are ready, check out: Kathryn’s cube of cheese solution.

N.B. I assume the puzzles written about are old puzzles. They are brought to Maths Jam meetings, or half remembered at the time, by attendees. If I have done something wrong by posting a puzzle here please tell me and I will be happy to correct the mistake.

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