Math Adventures - Toothpick Games

If you play a strategy game often enough, you start to see the best way to win. Sometimes it is best to go first, other times it is best to go second. Here are the directions for the toothpick games that we played.

Toothpick Game I
Play this game and find the winning strategy:
Take seven toothpicks and put them on the table between you and your partner.
When it is your turn, you must take ONE, TWO, or THREE toothpicks (your choice).
Whoever takes the final toothpick(s) wins.


Toothpick Game II
Let's change the rules a bit and see what happens. Does the strategy stay the same? Play this new version and find the winning strategy:
Again, start with seven toothpicks.
On your turn you must take ONE or TWO toothpicks.
Whoever takes the last turn wins.


Toothpick Game III
So, you figured out the winning strategy for Toothpick Games I and II? Let's change the rules a bit and see what happens. Play this new version and find the winning strategy:
This time, start with eight toothpicks.
On your turn you must take ONE, TWO, or THREE toothpicks.
Whoever takes the last turn wins.