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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: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughtssix or seven?Detti2005-01-10 21:59:08
Short and sweetSandeep2004-11-28 09:25:55
eight equal piecesvenkat v2004-07-24 14:14:15
simple may be bestJohn2003-12-24 22:32:47
Some Thoughtsre(3): define...-not so simpleTristan2003-12-13 00:58:27
Solutionre(2): define...Tristan2003-12-11 00:58:19
re: define...DJ2003-12-10 22:39:43
Questiondefine...Tristan2003-12-06 12:23:58
Some Thoughtsanother possible solutionjaypee2003-12-06 11:06:15
re(3): possible solutionjaypee2003-12-06 09:55:10
re(2): possible solutionjaypee2003-12-05 10:02:08
re(3): solutionBrian Smith2003-12-05 09:56:49
re(2): solutionSilverKnight2003-12-04 14:21:23
re: solutionEberhard2003-12-04 13:24:12
An ideaBrian Smith2003-12-04 12:45:38
re: possible solutionSilverKnight2003-12-04 12:28:37
possible solutionjaypee2003-12-04 11:31:32
SolutionsolutionCharlie2003-12-04 10:57:38
re: ThoughtsCharlie2003-12-04 09:16:40
Some ThoughtsThoughtsCharlie2003-12-04 09:07:02
re: Three cutsCharlie2003-12-04 08:50:24
SolutionThree cutsFederico Kereki2003-12-04 08:45:57
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