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Nim
Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The loser is the player who takes the last counter.
Age 7 to 18 Challenge Level:
Sprouts
This is a game for two players. All you need is paper and a pencil. The game starts by drawing three dots.
The first player has a turn by joining two of the dots and marking a new dot in the middle of the line. Or the line may start and end on the same dot.
OR 
When drawing a line, it cannot cross another line. (This is important to remember!)
A dot cannot have more than three lines branching to or from it. For example, in the game below, dots A and B cannot be used any more because they already have three lines.
The idea is to make it impossible for the other player to draw a line.
So the last person to draw a line is the winner. What are the winning tactics?
Does it matter who goes first?
Why must the game end after a limited number of moves? How many?
What happens when you start the game with four or five dots?
Why do this problem?
Possible approach
Key questions
Possible extension
Possible support
NRICH is part of the family of activities in the Millennium Mathematics Project.