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.

24 seconds