Boris has special digital watches. They are accurate, but instead of hours and minutes, they show two other numbers: the first is the sum of the digits that would normally be on the display, and the second is the sum of the hours and minutes (for example, at 7:30, they show 10:37).

What time could it be when Boris's watches show 6:15? Determine all possibilities.

(M. Dillingerová)

Hint. Can some digits in the normal time representation be ruled out in advance?
The sum of the digits showing the actual time is 6, so none of the digits is greater than 6. The sum of the numbers showing the actual hours and minutes is 15. Using the digits from 0 to 6, 15 can be expressed as the sum of two numbers in the following ways:

$$
0+15, \quad 1+14, \quad 2+13, \quad 3+12, \quad 4+11, \quad 5+10
$$

When Boris's clock shows $6:15$, it could be $0:15, 1:14, 2:13, 3:12, 4:11, 5:10, 10:05$, 11:04, 12:03, 13:02, 14:01, or 15:00.

Note. Part of the task is also to describe the process leading to the correct answer. The times listed without a proper explanation cannot be rated at the highest level.