Have You Got It? is an adding game for two players. You can play against the computer or with a friend. It is a version of a well known game called Nim.
Start with a target of 23.
The first player chooses a whole number from 1 to 4.
Players take turns to add a whole number from 1 to 4 to the running total.
The player who hits the target of 1 to 4 wins the game.
Play the game several times.
Can you find a winning strategy?
Can you always win?
Does your strategy depend on whether or not you go first?
To change the game, choose a new target or a new range of numbers to add.
Test out the strategy you found earlier. Does it need adapting?
Can you work out a winning strategy for any target?
Can you work out a winning strategy for any range of numbers?
Is it best to start the game? Always?
Consider playing the game where a player CANNOT add the same number as that used previously by their opponent.
Click here for a poster of this problem.