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Latin Numbers

Can you create a Latin Square from multiples of a six digit number?

Counting Factors

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

Hypotenuse Lattice Points

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

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.