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?
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594).
Whatever digits you choose the number will always be divisible by 7 and by 11 and by 13, in each case without a remainder.
Can you explain why?