DAY 421

HEADS OR TAILS

You are in a dark room and have 100 coins spread out in front of you. Ninety are facing heads up and ten are facing tails up. The coins are mixed up, and you cannot see which way they are facing. How can you sort the coins into two piles, such that each pile has the same number of coins facing tails up?

Answer:

Since the piles don't need to be the same size, make one pile of ten coins and one pile of the other ninety. Flip all of the coins in the pile of ten, and now both piles will have the same number of coins facing tails up.

Example:
Suppose you have three coins facing tails up in the pile of ten. This means there are seven coins facing tails up in the pile of ninety. If you flip all ten coins in the ten pile, you now have seven coins facing tails up - just as in the pile of ninety.

DAY 420

TWO BLIND MEN

A blind man goes to the mall and buys three pairs of red socks and three pairs of white socks. Another blind man is also at the mall, returning the three pairs of red socks and three pairs of white socks that he bought the day before. The two men bump into each other and all the socks are scattered on the floor, but each pair remains held together by a rubber band. The two blind men are able to gather the six pairs of socks together. Without any help, they are quickly able to sort the socks so that each man ends up with the same number and color of socks he started with - six red and six white. There is no indication on the socks as to their color. How do these two blind men do it?

Answer:

One of the men takes the rubber band off each pair. He keeps one sock for himself and gives the other to the other man.