Mathematics & Cake Cutting (Eight Pieces With Three Cuts)
Hi there. There was this post where one of the images featured cutting a cake into 8 pieces with three moves. This reminded me of a time where a few math majors friends were talking about this when they were discussing (math) game theory.
(I did not take any game theory courses myself but I have heard that this particular math field is interesting.)
Cutting Eight Cake Pieces With Three Moves
Suppose there is an Uncle Tetsu cheesecake that needs to be split into 8 equal pieces for 8 people. The cake has to be sliced in three moves only.
How can this cake be sliced in three moves?
Solution
If you cut only from above with three cuts, then you have six pieces. The way to do this is to recognize that cuts can be done sideways on the cake.
- The first two slices are from above which cuts the cake into quarters.
- The third and final slice cuts the cake in half from the side.
- This final cut turns the four cake pieces into eight.
Notes
The side cut could be done first with the next two slices from above.
With four cuts, you can have 16 slices. The first three cuts from above yield 8 pieces and the final cut is from the side.
This topic falls under fair division from math and economics (game theory). Fair division is also used for divorce settlements.
Nice post and the cake is yummy!