### Brain Teasers

# PIN the PIN !!!

Akash was trying to remember the PIN of his credit card. The PIN consisted of four characters, three of which were digits from 0 to 9 and one of which was a letter of the alphabet. If Akash can try different possibilities at the rate of 5 possibilities per minute and he works for 8 hours a day everyday, then find out the number of days in which he can try out all the combinations possible for the PIN.

### Answer

The number of days required to try all the combinations is 43 1/3 days.The four character code consists of 3 digits 0 to 9 and 1 letter of the alphabet A to Z.

Let us assume the first character of the PIN to be an alphabet and the remaining three characters to be digits.

Then the number of possible PINs

= 26*10*10*10

This is the number of PINs with the first character of the PIN being an alphabet.

However we can have the alphabet as the second character, third character or fourth character of the PIN. Thus there are four different combinations.

Hence the total number of such four character PINS available

= 4*26*10*10*10 = 104000.

At the rate of 5 possibilities, taking 8 hours a day, Akash would take

104000/(5*60*8) =

104000/(300*8) = 43 1/3 days.

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