Challenge Level

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?

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?

**Extension:**

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