Benny is a thief who tried to break into an Automated Teller Machine (ATM) using a screwdriver, but was only able to break five different keys on the numeric keypad and jam the card reader, at which point he heard Alice coming, so he hid. Alice walked up, put in her ATM card, successfully entered her 4-digit PIN, and took some cash. But she was not able to get her card back, so she drove off to
find help. Benny then went back to the ATM, and started entering numbers to try to discover Alice's PIN and steal money from her account. What is the worst-case number of PINs that Benny has to enter before correctly discovering Alice's PIN?
What will be an ideal response?
Since Benny broke 5 different keys and Alice was still able to enter her PIN, it
must only use the 5 remaining keys. So the total number of possible keys is now 54 = 625.
In the worst case, Benny will have to enter 625 before he enters the correct one.
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