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.)

I think the fewest number of pieces needed would be 5.  If you work out the are of the bun by using 3.14xr2 then the small bun would be 28.26, the medium 50.24 and the large one 78.50 making the total area 157 so that would mean each person needs an area of 39.25.  The first person gets the small bun and using one cut an area of 10.99 from the medium bun (2 pieces) That leaves an area of 39.25 of the medium bun which goes to the secong person(3 pieces) and as the large bun is 78.50 this just needs to be cut in half(5 pieces). I'm not sure how they work that out but I think it's the minimum number of pieces.

Posted by anne jackson on 2004-05-29 15:14:32