### 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?

### Bracelets

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

### 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?

# All the Digits

##### Age 7 to 11 Challenge Level:

Use counters or scraps of paper with the digits $0 - 9$ written on them.

Make a list of $3$ consecutive numbers $0 - 9$ remembering that $3$ has already been accounted for.

What could the ones digit of the product be if the multiplication is by $3$?

Which consecutive numbers could be in the four-digit number?

Which other digit could appear in the four-digit number?