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 Three cuts by Federico Kereki)

But is it possible to make three straight cuts vertically so that each piece has the same surface area on top and therefore the same volume as well?

(to get 7 equal-sized pieces, of course)
Edited on December 4, 2003, 8:53 am

Posted by Charlie on 2003-12-04 08:50:24