Finding passwords by random walks: How long does it take?

We compare an efficiency of a deterministic "lawnmower" and random search strategies for finding a prescribed sequence of letters (a password) of length M in which all letters are taken from the same Q-ary alphabet. We show that at best a random search takes two times longer than a "lawnmower" search.Comment: To appear in J. Phys. A, special issue on "Random Search Problem: Trends and Perspectives", eds.: MEG da Luz, E Raposo, GM Viswanathan and A Grosber