|Spoiler Inside: Solution to Puzzle||SelectShow>|
It is not possible.
The tens digit for the month must be 0 or 1. One person has one; one has the other. For the person having 1, the month’s ones digit must be 2 (as 0 and 1 are already used). That person must also have the day’s tens digit being 3 (as 0, 1, and 2 are already used), and thus the person’s day’s ones digit must be 0 or 1, but as both are already in use, this is an impossible situation.