To add to this excellent xkcd comic, the following site also exists : Password Haystacks.

Which is a stronger password?

T@+t0O

or

dudewhatdoesmytattoosay

(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.