If someone lost his password of his account to a website, but he is sure that the password is consisting of 3 digits without repeating of any digit, also he is sure that he used 2 numbers from (1 to 9) and 1 letter from ( T , I , U).
The website has a policy which let you try any incorrect password, but the is two conditions
- to enter any digit, you need 5 second then it will let you to write the next digit.
- each trial of an incorrect password freeze you for 1 second more than previous trail (for example, for 1st incorrect trial freezing for 1 sec , for 2nd incorrect trial freezes for 2 sec , for 3rd trail freezing for 3 sec, and so on until the end ……..).
The question is how much time it takes to check all the different trials if the correct password is the last trial ???
[toggle title=”Answer & Explanation” state=”close”]Answer : 60 h : 01 m : 48 s
Explanation:
As there will be 9 different numbers that 2 of them are used in the combination without repeating, it means that you have 9*8 = 72 probabilities to get correct answer ,
but there is a letter from (T , I , U) , it means there are 3 probabilities to get the correct letter, with combining them to the previous probabilities it means: 72 * 3 = 216,
and because the place of the letter is unknown it could be in any place first , second , or third digit so there will be 3 probabilities for each of the previous probabilities it means 216 * 3 = 648 probabilities to check,
As there is two conditions
1- Each digit from each probability need 5 seconds to let you enter next digit it means any probability with 3 digits, 1st digit doesn’t take time to enter as there is nothing before, then 5 seconds to enter 2nd digit then another 5 seconds to enter the 3rd digit , it means any probability need 10 seconds. 648 * 10 = 6480 sec
2- Each incorrect password (probability) increase 1 second of freezing, it means summation of the seconds from 1 to 647 (the last Trial Doesn’t need to be frozen as it is the correct one).
Summation from 1 to 647 = (647*648/2) = 209628 seconds
Totally = 209628+6480 = 216108 seconds
216108/(60*60) = 60.03
0.03 * 60 = 1.8
0.8 * 60 = 48
60 h : 01 m : 48 s
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