In article , Tristan
Miller writes
What about the easier problem of the shortest journey where every *line* is
visited? That is, what is the shortest journey such that the traveller
uses some portion of each of the Bakerloo, Central, Circle, District, East
London, Hammersmith & City, Jubilee, Metropolitan, Northern, Picadilly,
Victoria, and Waterloo & City lines at least once?

Why not the DLR as well?

There is admittedly some ambiguity here, since we can define "shortest" and
"visit" each in three different ways. Shortest can mean (a) least time,
(b) least distance, or (c) least number of station stops.

And for a particular line to be "visited", we could say that
the traveller either (1) travelled on that line's train between at least
two stops on that line, (2) travelled on a different line's train between
at least two stops on that line, or (3) set foot in or passed through a
station where that line stops.

Here's a route for (c)(1) that visits all 13 lines, travelling on each
for exactly one stop:

Bond Street or Tottenham Court Road
(Central) Oxford Circus
(Victoria) Green Park
(Piccadilly) Piccadilly Circus
(Bakerloo) Charing Cross
(Northern) Embankment
(Circle) Westminster
(Jubilee) Waterloo
(W&C) Bank
(DLR) Shadwell
(East London) Whitechapel
(District) Aldgate East
(H&C) Liverpool Street
(Metropolitan) Aldgate or Moorgate

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