II. Benny is a thief who tried to break into an Automated Teller Machine (ATM) u
ID: 3700811 • Letter: I
Question
II. 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?Explanation / Answer
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As Benny broke the five keys, we know that Alice’s PIN must composed of the remaining 5 keys on the numeric keypad which are not broken( because she was able to withdraw cash). As the PIN is of 4 digits in total possible keys will be = 5^4 = 625.
Hence for worst case, Benny has to enter 625 keys before discovering Alice's PIN.