## Nim-7

This is a basic form of the ancient game of Nim.

You will need seven objects, such as counters or blocks. It is a game for two players.

Place the 7 counters in a pile and decide who will go first. (In the next game, the other player will have the first turn.)
Each player takes turns to take away either one or two counters.
The player who takes the last counter wins.

Keep playing until you work out a winning strategy.
Does it matter who has the first turn?
What happens when you start the game with more counters?

There are more Nim-like games here .

#### Why play this game?

This game offers a motivating context in which children can improve their logical thinking skills.  It is a low threshold high ceiling game that is easily accessible but, at the highest level, has the potential to be generalised.

#### Possible approach

To start with, invite the children to play the game several times to get used to how it works. Everyone can have a go at playing randomly.

You may soon notice some of them start looking for a way to win so draw everyone's attention to this, using a mini plenary, and start thinking together as a class about how to win.  Look out for children who are discussing whether it matters who goes first and, again, draw everyone’s attention to this.

Encourage the children to record their moves and help them to articulate their ideas about strategy with sentences such as, ‘I noticed that when I ..., xxxx happened’.  Encourage them to think more than one step ahead:  ‘If I do this, then xxxx may happen and then I can xxxx. This would be useful because ...’.

Also encourage the children to articulate a hypothesis of ‘how to win’ and to try out their hypothesis a number of times.  If it fails, they need to develop a new hypothesis.  Children who think they have different winning hypotheses could play against each other and see what happens. Opponents will soon become partners in investigation as they test their hypotheses.  Children may like to try out their winning strategy at home or with a child in another class at playtime.

Encourage them to think abut how they can record their winning strategy, maybe in the form of 'Top Tips'.

#### Key questions

What happens when there are three counters left?
Does it matter who goes first?  Why or why not?
How can you win at this game?

#### Possible extension

You can encourage the children to think about ‘What if …?’ questions, such as what happens if you start the game with a different number of counters? (A series of key numbers will emerge, as well as some interesting observations about odds, evens and multiples.)

#### Possible support

You could offer to record a game for children who are struggling.  You can then look back together at key moments.  This might enable you to discuss what each player could have done differently at certain points in the game.