## 'Have You Got It?' printed from http://nrich.maths.org/

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 $23$ 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?

Tablet/Full Screen Version

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?

Extensions:

Can you use your knowledge of how to win the game to program our robot called AL to win?

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.