How Do I Find My Car?

Question

I have been discussing this problem with a coworker for a few days now and neither of us have made any headway on it. I would appreciate any help with a possible solution or maybe a suggestion of a book on related subject matter. The problem is as follows: I usually park my car near the doors of a convenience store but I constantly forget where my car is parked. Let's say that my car is parked somewhere on the real axis. Let's also assume that the probability distribution of my cars location is given by a normal distribution centered at zero. Starting at zero, I will walk along the real axis until I reach my car's position or turn around and walk back in the other direction. Given that I am extremely lazy, what is the optimal search strategy that minimizes the expected distance I have to walk?

Answer 1

The car is parked between -1 and +1 with 67% certainty per the empirical rule.

The car is parked between -2 and +2 with 95% certainty per the empirical rule.

There's your starting point....