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?
Is there an efficient way to work out how many factors a large number has?
What do products of 2, 5 and seven look like and how do they have multiples in common?