Saturday, May 27, 2006

A new one

Babies E and F (names have been shortened to protect the innocent) have 8 tupperware cups full of rice puffs. They know that one of the cups has a brownie in the bottom, but don't want to waste time eating the puffs to find it. The cups are the special kind with the lid that keeps the contents inside when inverted, so they can't just dump the cups out, although they certainly try.

They have a balance that they've learned how to use, and so they can weigh the cups against each other. They're getting quite impatient to find the brownie, and want to find it as quickly as possible. What is the minimum number of weighings that is required to find the brownie? They can weigh any combination of the 8 cups.

For example, they can put 1 cup at a time on each side of the scale until they find two cups that don't balance and they know the cup with the brownie is the heavy one. This of course is the incorrect solution, because it is only efficient if they get lucky and guess right the first time. The correct solution will work every time regardless of how they randomly select the cups to weigh.

-The Krunchy Krab

1 comment:

Bob said...

Weigh any 3 against any other 3 to start. If they balance, then it is one of the 2 left, and one more weighing will suffice.

If, however, one of the sets of 3 weighed is heavier than the other set of 3, then take any two of the heavier 3 and compare them. If one is heavier, there is the brownie. If they are even, then it is the odd one out of the heavier 3.

Regardless, only 2 weighings are required to identify the correct container.