Answer to the Math Problem of the Week for March 25, 2014

Question: Vinnie is a huge Yankees fan. He can win tickets to Opening Day if he solves the simple "Blue and White" test below: 

You are presented with three cloth bags. Each is marked "Blue", "White", or "Either". One bag contains only blue chips, one bag contains only white chips, and the third bag has both. All of the bags are marked incorrectly. You can choose one chip at a time, but cannot see beyond that chip to what else is in the bag. 

What is the fewest number of chips you can choose to re-label each bag correctly?

Answer:    1 chip

Vinnie should choose from the "Either" bag first. Since it is labeled incorrectly, it must be all blue or all white. Assume he chooses the blue chip. The "Either" label gets replaced by the "Blue" label on the first bag. If the Either and Blue labels were just exchanged, the third label would have had to be correct which is not true from the question. Therefore, the "Either" label goes on the third bag and the "White" label goes on the second bag. 

Incorrect Label  ->  Correct Label
Either  ->  Blue
Blue  ->  White
White  ->  Either

Vinnie answered one chip and will be watching the Yankees home opener on April 7!!!