My friend MF was invited to visit AF (another friend of mine).
At the entrance door to AF's place (apartment building with 36 tenants) there
was a 10 digit keyboard panel.
Noticing that only 2 keys showed signs of use and assuming that the 4 digit number usually represents someone's birthday date (either MMDD or DDMM), he keyed his guess and surprised AF by arriving without using the intercom.
Given that the code number is based on birth date and the "used keys" can be correctly detected, please answer the following questions:
1. What possible couples of digits enable a "first-guess" correct solution?
2. What is the worst case (i.e. the longest list of trials) for 2 "used digits"?
3. What is the best case for 3 "used digits" (defined for different triplets)?
4. What is the worst case for the above?