Greetings.

There's recently been much discussion here about the shortest (in terms of
time) possible London Underground journey such that every station is
visited.

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?

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. (In the case of
(c), no walking between stations is permitted, or else the problem is
trivial.) 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.

For example, here's one journey which attempts to satisfy definitions
(c.3), though I don't know if it's really the shortest:

1. King's Cross St. Pancras (Victoria, Northern, Hammersmith, Circle,
Metropolitan, Picadilly) to Whitechapel (East London, District) on the
Hammersmith & City Line: 6 stops, including Liverpool Street (Central)

2. Whitechapel to Liverpool Street on the Hammersmith & City Line: 2 stops

3. Liverpool Street to Bank (Waterloo & City) on the Central Line: 1 stop

4. Bank to Waterloo (Jubilee, Bakerloo) on the Waterloo & City Line: 1 stop

This is a total of 10 stops to visit all 12 LU lines. Can anyone find a
(c.3) route with less than 10 stops, or a route for any other combination
of definitions (a)-(c) and (1)-(3)?

Regards,
Tristan

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_V.-o Tristan Miller [en,(fr,de,ia)] Space is limited
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On Mon, 05 Jun 2006 23:56:38 +0100, Tristan Miller wrote:

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?

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. (In the case of
(c), no walking between stations is permitted, or else the problem is
trivial.) 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,

http://www.geofftech.co.uk/tubechall...sshortesttime/

(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.

For example, here's one journey which attempts to satisfy definitions
(c.3), though I don't know if it's really the shortest:

1. King's Cross St. Pancras (Victoria, Northern, Hammersmith, Circle,
Metropolitan, Picadilly) to Whitechapel (East London, District) on the
Hammersmith & City Line: 6 stops, including Liverpool Street (Central)

2. Whitechapel to Liverpool Street on the Hammersmith & City Line: 2 stops

3. Liverpool Street to Bank (Waterloo & City) on the Central Line: 1 stop

4. Bank to Waterloo (Jubilee, Bakerloo) on the Waterloo & City Line: 1 stop

This is a total of 10 stops to visit all 12 LU lines. Can anyone find a
(c.3) route with less than 10 stops,

Jubilee from Canada Water to Baker Street does it in 8 stops with no
changes. (Probably the quickest.)

Starting at Green Park: Jubilee to Waterloo, W&C to Bank, Central to
Liverpool St, H&C to Whitechapel. That does it in 6.

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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"Tristan Miller" wrote in message
...
Greetings.

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?

For example, here's one journey which attempts to satisfy definitions
(c.3), though I don't know if it's really the shortest:

1. King's Cross St. Pancras (Victoria, Northern, Hammersmith, Circle,
Metropolitan, Picadilly) to Whitechapel (East London, District) on the
Hammersmith & City Line: 6 stops, including Liverpool Street (Central)

2. Whitechapel to Liverpool Street on the Hammersmith & City Line: 2 stops

3. Liverpool Street to Bank (Waterloo & City) on the Central Line: 1 stop

4. Bank to Waterloo (Jubilee, Bakerloo) on the Waterloo & City Line: 1
stop

But you aren't really going through each line with that. You're going
through stations that have the required lines. Not the same thing surely.

Define "line"

Do you have to travel on both the Bank and Charing Cross branches
of the Northern ?

Is Metropolitan distinct from Hammersmith and City ?

If you travel between say GPS to Paddington D+C (three stops), does that
constitute traveling on the Circle, District, and Metropolitan, or just one
of those three ? If you travel between Edgware Road and Paddington D+C,
does that automatically cover both district and circle at the same time ?

Is the Wimbleware line separate from the "real" district line ? What
about Kensington Olympia ?

If you travel through the D+P station at Hammersmith, does that mean
you have "done Hammersmith" and thus done the H+C line, given that
those two may be separate stations ?

Richard [in SG19]



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In article , asdf
writes
http://www.geofftech.co.uk/tubechall...sshortesttime/

I see someone else already came up with my route. But note that this
one, unlike the others, goes on each line for exactly one stop.

--
Clive D.W. Feather | Home:
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Please reply to the Reply-To address, which is: