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Age 7 to 14 Challenge Level:
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 the Got It target $23$.
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 Got It target or a new range of numbers to add on.
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?
Away from the computer, challenge your friends:
One of you names the target and range and lets the other player start.
Extensions:
Can you play without writing anything down?
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 the opponent.
Click here for a poster of this problem.
NRICH is part of the family of activities in the Millennium Mathematics Project.