Here is a good shape problem I heard about recently:

There are 3 buns with sprinkles on the top that 4 people want to share. The buns have a radius of 3 inches, 4 inches and 5 inches, and although the people know where the center of each bun is, they don't know anything else about the buns, and all they have is a knife to divide the buns.

What is the fewest number of pieces required to let each person have the same area of bun? (Note that each cut must be from top to bottom; horizontal cuts would result in uneven sprinkle distribution. The cuts don't need to be straight.)

(In reply to another thought by ThoughtProvoker)

Five Easy Pieces (that was a movie title wasn't it?)

The problem is to find the minimum number of pieces (not cuts).  The problem states that "the people know where the center of each bun is".   It does not say that they are incapable of measuring angles.  So if they can find the center and also measure angles, then they can divide the middle bun into 25/32 and 7/32.

So just like Thought Provoker's 2nd comment, cut the big bun in half and give the 2 halves to persons A and B.  Give the little bun to person C.  Cut the middle bun into 2 pieces.  The larger piece measures 281.25 degrees, or 25/32 of the entire bun; this goes to person D.  The smaller piece goes to C.    Five Easy Pieces (easy if you can measure 25/32 and 7/32 of a circle)

And that's my story

Posted by Larry on 2004-05-07 23:15:02