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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.

Multiple Surprises

Age 11 to 16 Challenge Level:


Here are some challenges involving consecutive numbers and multiples.

Can you find three consecutive numbers where the first is a multiple of 2, the second is a multiple of 3 and the third is a multiple of 4?

Can you find several examples?
What do you notice?
Can you explain your findings?

What if the first is a multiple of 3, the second is a multiple of 4 and the third is a multiple of 5?

What if the first is a multiple of 4, the second is a multiple of 5, and the third is a multiple of 6?


Is there a way to find sets of four consecutive numbers which are multiples of 2, 3, 4 and 5 (in this order)?

Or five consecutive numbers which are multiples of 2, 3, 4, 5 and 6 (in this order)?


Can you use what you have discovered to help you find a few sets of ten consecutive numbers in which:

  • the first is a multiple of 1
  • the second is a multiple of 2
  • the third is a multiple of 3
  • ​​​​​​​the fourth is a multiple of 4
  • ​​​​​​​the fifth is a multiple of 5
  • ​​​​​​​the sixth is a multiple of 6
  • ​​​​​​​the seventh is a multiple of 7
  • ​​​​​​​the eighth is a multiple of 8
  • ​​​​​​​the ninth is a multiple of 9
  • ​​​​​​​the tenth is a multiple of 10?



With thanks to Don Steward, whose ideas formed the basis of this problem.