Possible password combinations? - formula to find all possible digit combinations
Hello,
I want a formula to tell me all the possible combinations for a password for multiple lengths. For example, if I were a 4-digit number that contains the numbers 0-9 on the formula, something like 10 ^ 4. Now we say the password can be 1 to 4 digits. The formula that I thought was:
10 ^ 1 + 10 ^ 2 + 10 ^ 3 + 10 ^ 4
This formula works very well for a four-digit number, but if the password can be up to 65 characters long, it becomes very difficult. Has anyone an idea?
Sunday, February 7, 2010
Formula To Find All Possible Digit Combinations Possible Password Combinations?
2 comments:
Any idea on the ground, I mean, if you let the number of different characters in all rated C and the total possible password L. While the total number of combinations:
C ^ ^ 1 + C 2 + C ^ 3 + .... + C ^ L.
What will be great.
Note that the closed form has become the sum of a geometric progression of a generic name:
Σ [k = 0 k to n] (a ^) = (a ^ (n + 1) - 1) / (a - 1)
And with a slight modification:
Σ [k = 1, n] (a ^ k) = (a ^ (n + 1) - a) / (a - 1) =
A = (a ^ n - 1) / (a - 1)
Therefore, the number of passwords with a length ≥ 1 and ≤ n-base number (leaving a 10 =) is:
a (a ^ n - 1) / (a - 1)
And the number of people with a length ≥ 1 and ≤ m:
Length ≥ 1 and ≤ m
Then, if n> m is the number of passwords with a length and m ≥ ≤:
a (a ^ n - 1) / (a - 1) - a (a ^ (m - 1) - 1) / (a - 1) =
= [A / (a - 1)] [Y ^ - a ^ (m - 1)]
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