x = 9 (mod 10)

x = 8 (mod 9)

x = 7 (mod 8)

x = 6 (mod 7)

x = 5 (mod 6)

x = 4 (mod 5)

x = 3 (mod 4)

x = 2 (mod 3)

x = 1 (mod 2)

This is part of a homework word problem from my class. I don't think the Chinese remainder theorem works since the modulo are not pairwise relatively prime. The only way I can think of solving it would take 30 minutes at least without a computer. So I'm wondering if there is a better way.

edit: I proved this must be one less than the least common multiple, i.e.

2519 (mod 2520)