Rule #1: Do not eat the game pieces (yet)! When we no longer
need them for class, you can take them home and enjoy, but in class they
are for the following counting game.
Playing Directions:
- Get into groups of two.
- Decide who goes first (flip a coin, or have the other person
guess in which hand you have the piece of candy).
- Put all the candy (_____ pieces) in a flat pile between the two of you.
- Starting with the first player, and alternating back and forth,
each player removes either 1, 2, 3, or 4 pieces of candy (you may not
remove 5 or more pieces, and you have to remove at least one piece
when it's your turn. Those are the only legal moves.
- The player who removes the last piece of candy (possibly along
with other pieces in a legal move) wins.
Classroom Instructions:
Play a series of games, keeping track of how many wins each
player has (make sure to decide at random each time, who goes first).
Challenge #1:
Try to find a Winning Strategy to this game.
Challenge #2: If you think you have a winning strategy, try
to verify that it really is -- can you mathematically prove
that if you follow this strategy then you will win? Can you find
algebraic equations which help give a precise picture of what is going
on?
Your in-class (and homework) assignment is to meet both of these
Challenges!
