Will Lil and Bill meet at the malt shop? This comes from page 38 of Digital Dice: Computational Solutions to Practical Probability Problems, by Paul J. Nahin. Check it out at amazon to get more puzzles like it.
Lil and Bill agree to meet at the malt shop sometime between 3:30 and 4:00 pm later in the afternoon. They're pretty casual about the details, because each knows that the other, while he or she will show up during that half hour, is as likely to do so at any time during that half hour as at any other time. If Lil arrives first, she'll wait 5 minutes for Bill, and then leave if he hasn't appeared by then. If Bill arrives first, however, he'll wait seven minutes for Lil before leaving if she hasn't appeared by then. Neither will wait past 4:00. what's the probability that Bill and Lil meet? What's the probability of their meeting if Bill reduces his wait to time to match Lil's (Both times are 5 minutes)? And if both times are 7 minutes?