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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?

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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?

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

Factor Trio

Stage: 2 and 3 Short Challenge Level: Challenge Level:1
45&= 3 \times 5^2\\
60 &= 2^2 \times 3 \times 5\\
91 &= 7 \times 13\\
105&=3 \times 5 \times 7\\
330 &= 2 \times 3 \times 5 \times 11

Therefore $105$ is the product of three distinct primes.

This problem is taken from the UKMT Mathematical Challenges.
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