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Adding All Nine

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!

N000ughty Thoughts

How many noughts are at the end of these giant numbers?

Mod 3

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

Big Powers

Age 11 to 16
Challenge Level

At first glance, a challenging problem; but no algebra is required to justify the solution.

Students who meet this problem for the first time may need a significant amount of support in structuring a solution so it is useful to be able to find similar tasks to which they may apply their new-found understanding.


It is important to be able to justify any pattern. How can you be sure it continues?