Cutting Cheese


I got this problem and its solution from Rustan Leino, who got this problem many years ago, likely from Jan van de Snepscheut.


You're given a 3x3x3 cube of cheese and a knife. Your goal is to divide the cheese into 27 1x1x1 cubes, using as few straight cuts as possible. You may not modify any piece of cheese's shape other than with a cut, and you may not move the cheese during a cut.

It's possible to do this with six cuts. Prove that it's not possible with fewer.

Solution     Reveal