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What if $\{$a tourist, a train addict, Dr. Sheldon Cooper, somebody who likesto waste time$\}$ wants to visit all metro lines or carriages in a givennetwork in a minimum number of steps? We study this problem with an applicationto the metro network of Paris and Tokyo, proposing optimal solutions thanks tomathematical programming tools. Quite surprisingly, it appears that you canvisit all 16 Parisian metro lines in only 26 steps (we denote by a step the actof taking the metro from one station to an adjacent one). Perhaps even moresurprisingly, adding the 5 RER lines to these 16 lines does not increase thesize of the best solution. It is also possible to visit the 13 lines of (thedense network of) Tokyo with only 15 steps.

The shortest way to visit all metro lines in a city