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Subj:     Slicing A Birthday Cake (S450b)
From: William Wu of U. C. Berkeley on 8/24/2005
At: http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml
Source: http://www.ocf.berkeley.edu/~wwu/riddles/easy.shtml#8wayCakeSlice

Birthday Cake Slicing Puzzle

You have a round birthday cake.  With three straight slices of a knife, divide the cake into 8 equal pieces. The author knows of two different solutions.

Jack's two solutions

To get eight slices each individual cut must halve the cake.  In addition, the plane of each cut must be perpendicular to the others.  So quarter the cake top with vertical cuts and halve the height with a horizontal cut for one solution.  The second solution is a vertical cut left to right and two diagonal cuts - top left to bottom right and top right to bottom left.

It should be noted that the first solution has equal shapes and volumes.  The second solution has equal volumes but different shapes.  Thank you Jack for this second solution.  I couldn't figure it out because of the shape differences.  I couldn't think out of the box.