### 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?

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

### Counting Factors

Is there an efficient way to work out how many factors a large number has?

# Have You Got It?

##### Stage: 3 Challenge Level:

Have You Got It? is an adding game for two players. You can play against the computer or with a friend. It is a version of a well known game called Nim.

Start with a target of $23$.

The first player chooses a whole number from $1$ to $4$ .

Players take turns to add a whole number from $1$ to $4$ to the running total.

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

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

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

Tablet/Full Screen Version

To change the game, choose a new target or a new range of numbers to add.

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

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

Is it best to start the game? Always?

Extensions:

Can you use your knowledge of how to win the game to program our robot called AL to win?

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