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.

Square Routes

Age 11 to 14 Challenge Level

i. How many four digit square numbers are composed of even
numerals?

ii. What four digit square numbers can be reversed and become the square of
another number? Can you explain why?