Fine, I'll do the math:
60 seconds in a minute (10 × 6)
60 minutes in an hour (9 × 5 × 4 / 3)
24 hours in a day (8 × 3)
7 days in a week (7)
6 weeks (3 × 2)
The bold 3's cancel out and become × 1, and then it's easy to see each integer from 1 to 10 appears exactly once when it's all multiplied together.

