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?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
For example, the third multiple of 6 is 18 which has six factors
(counting 1 and 18), while 17 and 19, the numbers on each side of
it, have two each being prime.