A thief broke into an Automated Teller Machine (ATM) using a screwdriver and was
ID: 3734105 • Letter: A
Question
A thief broke into an Automated Teller Machine (ATM) using a screwdriver and was able to jam the card reader as well as breaking five keys from the keypad. The thief had to halt the process of break-in and hide, as a customer approached to use the ATM. The customer was able to successfully enter their ATM card, punch in the 4 digit PIN and was able to draw out some cash. Since the card reader was jammed, the customer was however not able to withdraw the ATM card, and drove off to seek some help. In the meantime, the thief came back and decided to try to discover the customer’s PIN so that he can steal money from the customer. You are required to calculate the maximum number of PINs that the thief may have to enter before correctly discovering the customer’s PIN?
Explanation / Answer
The following points are provided in the question part:
A thief broke into an Automated Teller Machine (ATM) with the help of a screwdriver.
The thief jams the card reader and broke five keys from the keyboard in the ATM.
The thief stopped the process of breaking and hidden when a customer approached to use the ATM.
Since the card reader was jammed, the customer who put the card inside the machine was jammed. Therefore, the customer gone out to get some help.
PIN is a 4-digit number. So, the thief planned to try the PIN in meantime to withdraw money from that card.
The following is the calculation to find the maximum number of PINs that the thief may have to enter before correctly discovering the customer’s PIN:
PIN is a 4-digit number. The maximum number of PIN’s the thief can enter in a single digit of the PIN is 10 {0,1,2,3,4,5,6,7,8,9}.
The maximum number of PIN’s the thief can enter can be calculated as follows:
Each digit of the PIN can be filled with any of the 10 numbers.
10*10*10*10 = 10000.
It is provided that the thief broke 5 keys in the keypad.
The maximum number of PIN’s the thief can enter after breaking 5 keys in the keypad can be calculated as follows:
Each digit of the PIN can be filled with any of the 5 numbers.
5*5*5*5 = 625.
Therefore, maximum number of PINs that the thief may have to enter before correctly discovering the customer’s PIN is 625.
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