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A password contains 8 distinct digits. It takes 12 seconds to try one combination, what is the minimum amount of time required to guarantee access to database?
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A password contains 8 distinct digits. It takes 12 seconds to try one ...
Problem: A password contains 8 distinct digits. It takes 12 seconds to try one combination, what is the minimum amount of time required to guarantee access to the database?

Solution:

To guarantee access to the database, we need to try all possible combinations of the 8 distinct digits. Let's break down the problem into smaller steps to find the minimum amount of time required.

Step 1: Calculate the number of possible combinations
Since the password contains 8 distinct digits, we can choose any of the 10 digits (0-9) for each position in the password. Therefore, the total number of possible combinations can be calculated using the formula for permutations:

Number of combinations = 10P8 = 10! / (10 - 8)! = 10! / 2! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 = 1,814,400

Step 2: Calculate the time required to try one combination
Given that it takes 12 seconds to try one combination, we can say that the time required to try all possible combinations is:

Time required to try all combinations = Number of combinations x Time per combination = 1,814,400 x 12 seconds

Step 3: Convert the time to a more understandable format
The time calculated in the previous step is in seconds. To make it more understandable, let's convert it into minutes and hours:

Time required to try all combinations = 1,814,400 x 12 seconds
= 21,772,800 seconds
≈ 362,880 minutes
≈ 6,048 hours
≈ 252 days

Therefore, the minimum amount of time required to guarantee access to the database is approximately 252 days.

Conclusion: To guarantee access to the database, it would take approximately 252 days to try all possible combinations of the 8 distinct digits in the password, assuming it takes 12 seconds to try one combination.
Community Answer
A password contains 8 distinct digits. It takes 12 seconds to try one ...
24 seconds
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The chief scientist of a major vaccine producing company has the responsibility to keep the formula of the vaccine confidential. He stores the formula in his e-device with 3 consecutive locks, all of which need to be unlocked to access the formula. The first of the 3 locks is a pattern lock, the second one is a numeric lock and the third and final one is an alphanumeric lock. The pattern lock is in the form of a regular hexagon with 6 distinct vertices A1, A2, A3, A4, A5, A6, in that order. One needs to connect all the 6 vertices one after the another in any random order connecting each vertex only once and only one order of connecting the 6 vertices exists which will unlock the first lock. The numeric lock has a code of ABC, where A, B and C are single digit natural numbers. A is a multiple of 2. B is a multiple of 3, C is a multiple of 4 but not equal to A.The alphanumeric lock has a code MNPQRS, where M and N are alphabets and P, Q, R and S are digits. M and N have to be consecutive vowels or consecutive consonants, not necessarily in order. Two alphabets are said to be consecutive vowels if both of them are vowels and they are consecutive when all the 5 vowels are written in alphabetical order. For example, E and I are consecutive vowels, but A and O are not. Two alphabets are said to be consecutive consonants if both of them are consonants and they are consecutive when all the 21 consonants are written in alphabetical order. For example, D and F are consecutive consonants but D and V are not. For example, M and N can be A and E respectively or E and A respectively. P is equal to Base-Ten-Index of M. Q is equal to the Base-Ten-Index of N. R and S can only take binary values, that is, 0 or 1.Base-Ten-Index of an alphabet = Index of alphabet % 10, where Index of an alphabet is its position when all alphabets from A to Z are arranged alphabetically and a%b is the remainder when a is divided by b.For example, Base-Ten-Index of J = 10 = 0 , Base-Ten-Index of M = 13 = 3.The chief scientist can only set passwords/patterns which follow all of the conditions mentioned above.Based on the information given above, answer the questions that follow.Q.Given below is a list of patterns/passwords, some of which are in accordance with the rules mentioned and some are not. The chief scientist can use any combination of valid patterns/passwords from the following to lock the e-device. What is the total number of ways in which he can do so?Pattern:(1) A1 A2 A5 A6 A5 A2 A4 (2) A1 A2 A3 A4 A5 A6 (3) A6 A5 A4 A3 A2 A1 (4) A1 A6 A5 A2 A4Numeric password:(1) 234 (2) 434 (3) 298 (4) 634 (5) 894 (6) 230 (7) 638Alphanumeric password:(1) AE1500 (2) CD3410 (3) HJ8000 (4)QP7600 (5) AB1211 (6) YZ4600 Correct answer is '40'. Can you explain this answer?

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A password contains 8 distinct digits. It takes 12 seconds to try one combination, what is the minimum amount of time required to guarantee access to database?
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