To add to this excellent xkcd comic, the following site also exists : Password Haystacks.
Which is a stronger password?
(Click to find out, I’ll wait).
Pretty sweet indeed. What a difference.
Anyways, the reason I’m linking this stuff is that this would make a great lesson in exponents. While the first password uses far more letters and symbols, so it has a large base, since the power is only 6 there aren’t as many permutations to try. But the second password’s power of 23 fully compensates for the smaller base of letters to check.
The buy-in for this type of problem is that I’d bet that most students would pick T@+t0O as the stronger password. It’s a fun day in math class when you can fight (false) intuition.
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