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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?

Flashing Lights

Age 7 to 11 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?

Flash

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?