AMO 2027 Grades 8-9 SET 10 - Self-study Question 3

Find how many three-digit numbers satisfy all the following conditions:
- if it is divided by 2, the remainder is 1,
- if it is divided by 3, the remainder is 2,
- if it is divided by 4, the remainder is 3,
- if it is divided by 5, the remainder is 4,
- if it is divided by 8, the remainder is 7.