A Combinatorial Solution for Bridge and Torch Problem

Abstract

In this note we give a combinatorial solution to the general case of the puzzle known as “bridge and torch problem”. It is about finding the shortest time needed for n people to cross a bridge knowing that at most two persons can walk together on the bridge (at the speed of the slowest) and, because it is dark, a torch is needed for each crossing (and they have only one torch). The puzzle can be seen (and solved) as a discrete optimization problem.