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 re: possible solution by SilverKnight)

I was taking into account the two cuts already made in the cake, dividing it into four equal pieces.Then by making three additional cuts in the cake as I described it would divide the cake into eight pieces.
for the pieces to be equal the three additional cuts would have to be bisecting the right angles created by the first two cuts. But if you are talking about ONLY three cuts then my thinking is incorrect.

Posted by jaypee on 2003-12-05 10:02:08