SLD
Contributor
Ok. Slice a cube with 5 straight cuts. What’s the maximum number of pieces of whatever size or shape that you can make. Is it 32? I.e. can you cut it in such a way that every cut is making a division of every piece so you get 2^5 pieces?
Or is it less than that? I was thinking of cutting along the diagonals of each face. There are three basic faces to cut (because the cuts go all the way through). So the first four cuts should create 16 pieces. But will one more cut along a diagonal of the uncut face divide every piece? It’s hard to visualizes that point. My son says no, just half of them, so you only get 24 pieces. And that’s the maximum. But one could cut from one corner to the opposite.
I tried to do it on a real stick of butter as that’s how the problem was first posed to me. I found that’s a good way to piss of your wife for wasting a stick of butter. But that’s all I discovered.
SLD
Or is it less than that? I was thinking of cutting along the diagonals of each face. There are three basic faces to cut (because the cuts go all the way through). So the first four cuts should create 16 pieces. But will one more cut along a diagonal of the uncut face divide every piece? It’s hard to visualizes that point. My son says no, just half of them, so you only get 24 pieces. And that’s the maximum. But one could cut from one corner to the opposite.
I tried to do it on a real stick of butter as that’s how the problem was first posed to me. I found that’s a good way to piss of your wife for wasting a stick of butter. But that’s all I discovered.
SLD
