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
If my logic was correct in stating that a 7-piece solution is impossible (considered as a 2-D problem with vertical cuts), then what remains, to answer the question, is the 6-piece solution, which there are various ways of accomplishing, such as a radially symmetric asterisk-like 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 2003-12-04 09:16:40