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.

Another way of cutting the cake is as follows:
Since a cake has height make one cut cutting the height in half. Then make the other two cuts as described in the second paragraph of the posted problem. This will divide up the cake into 8 eqaual pieces, though the bottom pieces will not have a lot of icing on them.

Posted by jaypee on 2003-12-06 11:06:15