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?

Special Sums and Products

Age 11 to 14 Challenge Level:

The numbers 4 and 12 have a special property.

$$\begin{eqnarray} 4 + 12&= 16\\ 4 \times 12&= 48 \end{eqnarray}$$
and 16 is a factor of 48.

Find some other examples of pairs of numbers such that their sum is a factor of their product.

What condition must exist for pairs of numbers to be related in this way?