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!

Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.

What an Odd Fact(or)

Age 11 to 14 Challenge Level:

What can you say about the patterns in the last digits of powers
of $2$, $3$, $4$ etc?

How can you use these patterns to say what the last digits are
of the numbers raised to the power $99$?

Now can you say whether the sum is divisible by $5$?