### 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?

### Sweets in a Box

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

### Maze 100

Can you go through this maze so that the numbers you pass add to exactly 100?

# Balance of Halves

##### Stage: 2 Challenge Level:

We had this solution sent in from Emma at Kelso State School

1. You could put two on 3$\frac{1}{2}$.
2. You could also put one on the $\frac{1}{2}$ and the 6$\frac{1}{2}$.

Summer and Yesha at Valence Primary School sent in the following:

7 = 0.5, 6.5
= 1.5, 5.5
= 2.5, 3.5

7 = 14 halves

Boyang from Mountfields Lodge and Caroline from St Jude's C of E School looked at this problem very logically. To balance 7 on the left using two "half" weights on the right, Boyang told us:

The two numbers on the right hand side could be:

$\frac{1}{2}$ + $6\frac{1}{2}$
$1\frac{1}{2}$ + $5\frac{1}{2}$
$2\frac{1}{2}$ + $4\frac{1}{2}$
$3\frac{1}{2}$ + $3\frac{1}{2}$
$4\frac{1}{2}$ + $2\frac{1}{2}$
$5\frac{1}{2}$ + $1\frac{1}{2}$
and finally, $6\frac{1}{2}$ + $\frac{1}{2}$.

I wonder whether the first solution is different from the last one? What do you think?

Caroline wasn't sure whether you are allowed two weights on the same hook, but I think that's fine.

Nobody has looked at hanging three weights on the right-hand side, or having quarter divisions on the balance. If you do investigate these situations, let us know! Please don't worry that your solution is not "complete" - we'd like to hear about anything you have tried.  Teachers - you might like to send a summary of your children's work.