The wives/keys problem sounds like the "Matching Birthdays" problem. I think that this was a favorite one of Einsteins. From memory, I think it works out that at a dinner party with 22 people it is better than even odds that two people will have the same birthday. I think (if you wuz a gambling person) you can make money at this. There are however two caveats.
1. I can't remember the exact numbers so check them out before putting your money on the line.
2. I've never tried it because I never get invited to dinner parties with that many people. Come to think of it, I never get invited to dinner parties.
