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Piece o' Cake (Posted on 2003-12-04) Difficulty: 3 of 5
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(3): possible solution | Comment 13 of 22 |
(In reply to re(2): possible solution by jaypee)

If you're using only three cuts in the cake the greatest number of pieces that can be created with equal volume would be 6. One cut would be through the center of the cake, forming a diameter. The other two cuts would be made perpendicular to the first cut, creating two chords to the circle. One chord would be on one side of the center at a distance "x" from the center and the other chord would be on the other side at a distance "x" from the center. This would create two equal chords. The question is what is distance "x" so that the three cuts create six pieces of equal volume? That I haven't determined yet.
  Posted by jaypee on 2003-12-06 09:55:10

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