I was sitting down with Stefanie one day to share a round cake (our birthdays are only two weeks apart). "This is easy enough," I said, "one cut right through the middle divides the cake into two equal pieces."
Then, two more people showed up, but I was undaunted. Two straight cuts will divide the cake into four equal parts, I thought.
Then, I saw another car pulling up. I remembered that three straight lines can divide a circle into at most seven parts, but I was unsure if that could be done so that all the pieces are equal (in volume, not necessarily in shape).
How can I use three straight cuts to divide our cake into all equal parts and accomodate the greatest number of people?
Note: since Stefanie spent so much time decorating the cake, I don't want to rearrange the pieces when I cut them.
(In reply to
Thoughts by Charlie)
If my logic was correct in stating that a 7piece solution is impossible (considered as a 2D problem with vertical cuts), then what remains, to answer the question, is the 6piece solution, which there are various ways of accomplishing, such as a radially symmetric asterisklike set of cuts, or dividing in half and then making two cuts perpendicular to the original diameter cut, with appropriate distances figured out.

Posted by Charlie
on 20031204 09:16:40 