Answer
No, it would not be feasible to generate and test all possible passwords of length 10 or less in under one week's time.
Work Step by Step
Total characters available: 26 uppercase letters + 26 lowercase letters + 10 digits + 3 special symbols = 65 characters.
Total number of possible passwords of lengths 1 through 10:
$ 65 + 65^2 + 65^3 + \ldots + 65^{10}$
- \( 65^1 = 65 \)
- \( 65^2 = 4,225 \)
- \( 65^3 = 274,625 \)
- \( 65^4 = 17,851,625 \)
- \( 65^5 = 1,160,355,625 \)
- \( 65^6 = 75,423,115,625 \)
- \( 65^7 = 4,902,502,515,625 \)
- \( 65^8 = 318,662,561,515,625 \)
- \( 65^9 = 20,713,066,497,515,625 \)
- \( 65^{10} = 1,346,349,295,838,515,625 \)
Sum of possible passwords \( \approx 1.371 \times 10^{18} \) passwords
The password-cracking tool can test 10,000,000 passwords per second. So the total time required is the total number of passwords divided by 10,000,000.
Time required: \( = \frac{1.371 \times 10^{18}}{10,000,000} \) \( \approx 1.371 \times 10^{11} \) seconds
\( = \frac{1.371 \times 10^{11}}{60 \times 60 \times 24} \) \( \approx 1,587,500 \) days
Since one week is 7 days, it's clear that testing all possible passwords of length 10 or less would take far longer than one week.
