Challenge: how many combinations? (car immobilizer)
in my car i have a combination-lock immobilizer.
the combination lock is built like so:
   
four keys. each key however, holds more than just one digit:
   
so a combination might be:
now, one might think that this can be used to reduce the number of times you have to hit every key when you brute-force the device, as the same keys would be hit for different digits.
1. what is the minimum number of combination for brute-forcing the lock? how so?
2. the lock “locks up” for a few minutes (say, 3) after 3 failed attempts, how would this effect your method, if at all?
this is a rather easy one, but it may surprise you. i will post a follow-up once this one is solved to my satisfaction.
solutions are to be emailed to me directly rather than put in a comment.