Mathematically Optimal Ways to Escape A Car When It’s Raining And You Forgot The Umbrella

It happened again. You didn’t notice the gloomy skies as you pulled out of your driveway to go to Home Depot, and now you’re umbrella-less and sitting in their parking lot, watching the raindrops bead up and flow down your windshield. Worse yet, their New Grill November sale has summoned every dad within a 25 mile radius to the store, forcing you to park in the back of the lot. You didn’t even bring your rain jacket, because it’s new and you didn’t want to dirty it while carrying your new oak floorboards.

As you sit there feeling sorry for yourself, you notice that the sound of the rain has changed. From the time you pulled in to the moment you searched Amazon for oak flooring, the intensity of the rain has changed, and with it, the sound. That’s it! All you have to do is pick the right time to make a mad dash for the those automatic doors, and you’ll get minimally wet, despite making no preparations. You listen closely, and think back to a familiar math problem…

Secretary Problem

Let’s say you are the CEO of a large floorboard manufacturing plant, and the paperwork has really been piling up. You need a secretary, so you put out an ad in the classifieds: “SKILLED SECRETARY WANTED.” It’s a small town, so you don’t expect it to be too hard to choose one candidate from the applicants.

On the day of the interviews, to your surprise, the town has been able to come up with a huge line of secretaries, all with varying skill levels for working with large quantities of paperwork. You have enough experience to objectively rank each secretary against the others you’ve already interviewed, however, each of the potential secretaries is impatient and must be given a hire offer or rejection at the end of their interview. In addition, the dejected rejects will leave town as soon as they are rejected, so you can’t even call them back after the process. How can you hire the best secretary when you don’t know until the very end which secretary was the most skilled choice?