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

Hey there!

A thief broke out 5 keys. We know that Pin is of 4 characters and all should be numerical.

In a ATM keyboard, We have 10 digits : 0 , 1 , 2 ,... 9 .

So out of ten keys, 5 are broken .
5 keys are remaining. Yet customer could take money.

So, customer pin is in the 5 remaining keys.

So, We have to find the number of ways he can choose 4 numbers from 5 .

For the first key, We can select out of 5 , For the second 5 .

So, The number of ways 4 keys can be selected from 5 = 5P4 = 5*4*3*2 = 120.

The maximum number of times the guy must enter before getting right one = 119 .

Hope helped!