Riddle Ye! Answers
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Person #1 cuts off what he believes to be a third. #2 takes either the third or the two thirds. #1 keeps the other one. Whoever has the two thirds divides it with #3 in the original half-cake way.
–Shish—
Okay, three hungry Kids: A, B and C. How about we have Kid B decide which of the other two cuts the cake… If he picks Kid C, then Kid C cuts the cake into what he perceives to be three precise slices. Because the task of equivalency is Kid C’s alone, he gets the last slice. Since Kid B has chosen who will cut the cake, but has not cut it directly, he can be said to have had partial authority. He gets to choose his piece before Kid C. But Kid A, having had no real authority in the decision-making processes, gets first choice of slice. Does that sound logical?
–CU, of EveryNothing.comP.S. It goes without saying that these rules must be explained to the Kids beforehand. We can assume that at least one of them will volunteer to function as Kid B.
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A friend of mine and I discussed the cake problem today on break and we came up with this solution. In order to cut the cake into 3 equal pieces, you would need to give each person a knife and tell them that they will each make a cut and when the cake is cut, each person will take the slice of cake opposite to their knife. The people are instructed to cut the cake in this way: Each person puts their knife above the cake, simulating where it will be cut. By cooperating with the other two people, all three agree on where their own knife and the other knives should be in relation to the other two before they cut knowing that they will be receiving the piece opposite to their knife, a piece which they themselves are not cutting. By giving all of the people the same amount of power in determining how the cake is cut in conjunction with a person receiving a piece of cake their knife did not participate in making, you are assured that the combined efforts of all three will insure the cake is cut into thirds as perfectly as it can be.
–d00m
1:00am (GMT +10.00) tomorrow 
