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!
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
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.
rom Hethersett High School, Norwich used algebra and found the
fourth root of 331776, namely 24 - sort of hidden
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