If Denmark is anything like Sweden there's also:
- SSN from different ID space gets assigned to immigrants; when they become citizens they are assigned a new permanent SSN.
- SSN:s have a long and a short form; the short form which cuts off century information can be the same for someone who is 5 years old and someone who is 105 years old.
- When an unconscious patient comes in to the E.R. you don't know their SSN, so a temporary one is assigned for use in patient records. Such temporary SSN:s are not coordinated nation-wide so multiple patients may have the same SSN. In some hospitals they don't even have a local standard for ID:s. The staff just makes something up on the spot. It happens that the SSN they made up collides with a valid SSN for another person.