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?

Flashing Lights

Stage: 2 Challenge Level:

Norrie is watching the aircraft warning lights on the tops of some tall buildings in the city. He sees two lights flash at the same time, then one of them flashes every $4$th second, and the other flashes every $5$th second.
How many times do they flash together during a whole minute?

Norrie then watched a third light. He saw it flash at the same time as the other two, then flash every $7$th second. How many minutes before this light again flashes at exactly the same time as the other two?