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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 11 to 16
Challenge Level
Why play this game?
Sprouts offers an engaging introduction to networks, encouraging students to experiment and conjecture. The challenges requires them to work systematically, refine ideas, and eventually find a winning strategy.
Possible approach
Introduce the game to the class by inviting two volunteers to play against each other. Do this a couple of times, giving each the opportunity of going first.
Ask the students to play the game in pairs. Challenge them to find a winning strategy. As they play, circulate around the classroom and ask them what they think is important.
After a suitable length of time bring the whole class together and invite one pair to demonstrate their strategy, explaining their decisions as they go along. Use other ideas to refine the strategy.
Once students are confident about their strategies they could move on to exploring what happens when the game starts with four or five dots.
Key questions
Does it matter who goes first?
Why must the game end after a limited number of moves? How many?
Possible support
You can begin by playing with just two dots at the start.
Possible extension
NRICH is part of the family of activities in the Millennium Mathematics Project.