Math in… Road Trip Restaurants

If you want a nice road trip meal without needing to backtrack along the highway, it turns out the mathematical constant e = 2.7182818284… can help!

Strategy: If you know you’re going to pass n exits, skip the first k exits and then exit at your next favorite restaurant that you’ve seen so far — or at the last exit, in a pinch.

How many exits should you skip for the highest probability of having the best meal? If n is large, a result from optimal stopping theory says skipping k = n/e exits gives about a 1/e = 0.3678794411… probability of stopping at the best one. In other words, after skipping about 37% of the exits there is about a 37% chance that the next best restaurant you see will actually be your favorite restaurant on the trip!