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 Piece o' Cake (Posted on 2003-12-04)
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.

 See The Solution Submitted by DJ Rating: 3.6667 (9 votes)

 Subject Author Date six or seven? Detti 2005-01-10 21:59:08 Short and sweet Sandeep 2004-11-28 09:25:55 eight equal pieces venkat v 2004-07-24 14:14:15 simple may be best John 2003-12-24 22:32:47 re(3): define...-not so simple Tristan 2003-12-13 00:58:27 re(2): define... Tristan 2003-12-11 00:58:19 re: define... DJ 2003-12-10 22:39:43 define... Tristan 2003-12-06 12:23:58 another possible solution jaypee 2003-12-06 11:06:15 re(3): possible solution jaypee 2003-12-06 09:55:10 re(2): possible solution jaypee 2003-12-05 10:02:08 re(3): solution Brian Smith 2003-12-05 09:56:49 re(2): solution SilverKnight 2003-12-04 14:21:23 re: solution Eberhard 2003-12-04 13:24:12 An idea Brian Smith 2003-12-04 12:45:38 re: possible solution SilverKnight 2003-12-04 12:28:37 possible solution jaypee 2003-12-04 11:31:32 solution Charlie 2003-12-04 10:57:38 re: Thoughts Charlie 2003-12-04 09:16:40 Thoughts Charlie 2003-12-04 09:07:02 re: Three cuts Charlie 2003-12-04 08:50:24 Three cuts Federico Kereki 2003-12-04 08:45:57

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