Here's another brain teaser I like to use during interviews ([[How to Handle Interviews]])...I call it "rejection letters." This is very similar to the Monty Hall Problem. I like to ask this brain teaser when a candidate is cocky or claims to never make mistakes or not need assistance. Or I'll ask the candidate a question like, "When you have a difficult problem and you just can't find a solution on your own, when do you seek assistance?" The question and it's answer are meaningless to me, I'm simply using this as a segue to the problem:
I think you are a strong candidate and I'd like to offer you a job. Assume there are 3 envelopes in front of you, 2 have a rejection letter and 1 has the offer for employment. Assume you really want to work here. Pick an envelope. Now assume I know which envelopes have the offer and rejection letters. I'm now going to show you that one of the other envelopes is a rejection letter. I'm going to offer you a chance to change your envelope choice, is that a wise idea and why?
I give no hints, remember, the goal is to have the candidate seek assistance. Very few people can explain why it is a bad idea at this point, even if they know the Monty Hall Problem. I ask for probabilities of the outcome and I've never heard an answer yet that wasn't 1 in 3 for both choices. I continue...
New game, assume I have 4 envelopes, 3 are rejection letters. You pick one, I show you 2 others that are rejection letters and offer you the chance to change your choice. Do you and why or why not?
Again, I ask for probabilities. I've always still heard 1 in 4.
I ask again using 5 envelopes/4 rejection letters. By now every candidate was visibly anxious probably trying to figure out what is going on. Still I give no hints and still I always get the 1 in 5 answer.
I continue to 6 envelopes/5 rejection letters. If the candidate hasn't asked for assistance or has not spotted the trend I go right for 100 envelopes/99 rejection letters. By now everyone has spotted the trend and can get the answer (if you switch your choice your odds drop to 1 in 2 immediately). But every candidate has failed in my opinion...no one has asked for help early.