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?

Stair Climb

Stage: 2 and 3 Short Challenge Level:

Boris has to run up $99$ steps, and runs up $5$ in each unit of time, so it takes him $99 \div 5 = 19\frac{4}{5}$ units of time to reach the top.

Spike has to run up $78$ steps, and runs up $4$ in each unit of time, so it takes him $78 \div 4 = 19\frac{1}{2}$ units of time.

Percival has to run up $61$ steps, and runs up $3$ in each unit of time, so it takes him $61 \div 3 = 20\frac{1}{3}$ units of time.

Therefore they finish in the order Spike, Boris Percival.

This problem is taken from the UKMT Mathematical Challenges.
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