What time should the last watch show?

Key insight: each time is made by adding 1 to every digit of the previous time and then rotating the three digits one place to the left.

• Example: 1:20 → digits 1, 2, 0. Add 1 to each → 2, 3, 1. Rotate left → 3, 1, 2, which gives 3:12.

• Example: 3:12 → digits 3, 1, 2. Add 1 → 4, 2, 3. Rotate left → 2, 3, 4, which gives 2:34.

• Final step (to get the missing time): 4:53 → digits 4, 5, 3. Add 1 → 5, 6, 4. Rotate left → 6, 4, 5, which reads 6:45.

Answer: 6:45.