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!

Is there an efficient way to work out how many factors a large number has?

Even So

Age 11 to 14 Challenge Level

Find some triples of whole numbers $ a $, $ b $ and $ c $ such that
$ a^2 + b^2 + c^2 $ is a multiple of 4. Is it necessarily the case
that $ a $, $ b $ and $ c $ must all be even? If so, can you
explain why?