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?

Answer 1

in the pin all the numbers r der accept the buttons which are broken

Answer 2

For the first digit of the PIN we have 10 options- 0,1,2,3,4,5,6,7,8 & 9.


For every option for the first digit, we have 10 options of the second digit.
Thus we have maximum 10*10=10² options for the first two digits.

Using the same argument, we have 10²*10=10³ options for first 3 digit and for a four digit PIN we have 10³*10=10⁴ or 10,000 options.

Therefore the thief may have to enter maximum 10,000 numbers of pin.