Aim
Play the coin games and work out the best strategies to win.
What To Do
I took the following game from a Julia Robinson Maths Festival problem set.
Game 1 - Take 1 or 2 pennies
The game is played with 2 people.
Start with a known number of pennies.
Each turn a player can take 1 or 2 pennies from the pile.
The player who takes the last coin(s) wins.
What is the best strategy to win? Do you want to go first or second?
Start with 3 coins in the pile and work your way up to help decide the best approach to win.
Game 2 - Take 1, 2 or 3 pennies
Same as the last game, except this time you can take 1,2 or 3 pennies at a time
Again, what is the best strategy to win? Do you want to go first or second?
Start with 4 coins in the pile and work your way up to help decide the best approach to win.
Game 3 - Take 1 or turn 1
Start with all the pennies heads up
Same as a above except this time you can either take one penny or flip it to tails. You can not flip it back from tails to heads.
Again, what is the best strategy to win? Do you want to go first or second?
Start with 2 coins in the pile and work your way up to help decide the best approach to win.
Inspiration