You could write this problem out as 1x 3 x
4x 6 x 7 x 8 x 9 x (2 x 5) x 10. The
product of the first seven numbers is not a multiple of ten, but
the last part gives us 10 x 10 so the overall product must be a
multiple of 100, but not a multiple of 1000. So the answer is two
This problem is taken from the UKMT Mathematical Challenges.