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### Number and algebra

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# Sprouts

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### Nim

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

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Age 11 to 16

Challenge Level

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?

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.