Problem of the Week-4

A coin Trick

Alice tosses 17 coins onto a table top. She closes her eyes and instructs Bob to turn over as many coins as he likes. Bob can, if he wishes, turn over the same coin every time or any number of times, but there is a proviso: Every time a coin is turned Bob must say out loud the word "flip".

When finished Bob covers one coin with his hand and tells Alice it is okay to open her eyes. Alice then swiftly, and correctly, announces that state of the coin under Bob's hand, whether it is heads up or tails up. Alice is able to do this correctly every time the game is played, even if a different number of coins is used. What is Alice's trick? Explain.

Posted: 10/13/03

Submit your answers (by e-mail or hard copy) before 4 pm on 10/24/03 to Noah Aydin.

Mathematics Dept.