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!
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
The solution is based on the divisors of 24.
i.e 1 x 2 x 3 x 4 x 6 x 8 x 12 x 24 = 331776
Alison at Maidstone Girls Grammar School arrived at her solution by trial and improvement techniques and had found that the divisors of 30 were too big when multiplied together and the divisors of 20 too small. She had ascertained that 24 did have quite a lot of divisors compared to others in this range.
Gareth rom Hethersett High School, Norwich used algebra and found the fourth root of 331776, namely 24 - sort of hidden inside:
Let a, b, c, d, e, f, g, and h be the divisors where a x b x c x d x e x f x g x h = 331776 and a = 1.
But a x h = h; b x g = h; c x f = h and d x e = h
hence h x h x h x h = 331776
and so h = 24