### 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?

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

### Have You Got It?

Can you explain the strategy for winning this game with any target?

# Factor Trio

##### Stage: 3 Short Challenge Level:
\begin{align}
45&= 3^2 \times 5\\
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
\end{align}

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

This problem is taken from the UKMT Mathematical Challenges.