### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

### It Figures

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

### Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

# GOT IT Now

##### Stage: 2 and 3 Challenge Level:

The game Got It is a version of a well known old favourite called Nim.
It is an adding game for two. You play against the computer or against a friend.

Start with a target of $23$. Set the range of available numbers from $1$ to $5$.
Players take turns to add a whole number from $1$ to $5$ to the running total.

The player who hits the target of $23$ wins the game.

Play the game several times. Can you always win?
Can you find a winning strategy?

Does your strategy depend on whether or not you go first?

Change the game, choose a new GOT IT! target.

Test out the strategy you found earlier. Does it need adapting?

Can you work out a winning strategy for any target?

Is it best to start the game? Always?

Change the game again, returning to a target of $23$ but using a different range of numbers this time.

Test out the strategies you found earlier. Do they need adapting?

Can you work out a winning strategy for any range of numbers? Is it best to start the game? Always?

Can you work out a winning strategy for any target and any range of numbers?

Extensions:

Can you play without writing anything down?

Target $24$ using either a $1$, $3$ or $5$. What is the strategy now?

Consider playing the game where a player CANNOT add the same as that used previously by the opponent.

Play NIM.