Los Angeles Math Circle

9/23: Circle meeting (Olga Radko)

Win at Nim!
We will explore the famous game of Nim. After learning the rules and playing it several times, we will see that it is not easy to predict who has an advantage (first or second player) in each starting position. It is remarkable that the winning strategy for the game can be formulated using the binary system of notation for numbers. We will review the binary notation, formulate the winning strategy in Nim, and see why and how it works. As a homework, teach your family and friends to play (and win!) in the game of Nim. For more details, you can consult the wonderful books by Martin Gardner \"Mathematical puzzles and diversions\" and \" New mathematical diversions from Scientific American\", or find information on the Internet. (You can even find a place to play the game online).