Thursday 28 January 2016

The "All Lines Challenge"

This is how I worked out possible routes. I'm concentrating on going one stop per line. I'm assuming that there is no perverse reason why going two stops at any time is faster.

The limiting factor is the Waterloo & City line with it's two stations, so Waterloo and Bank must be on your itinerary.

From Bank, you must go north or you won't be able to tick off the Metropolitan line at all. Your one-stop options are Central line to Liverpool Street and Northern line to Moorgate. Then the obvious thing is to head west/anti-clockwise for three consecutive stations to tick off the Circle, Hammersmith & City and Metropolitan lines, either Liverpool Street to Farringdon or Moorgate to King's Cross St. Pancras.

From Waterloo, you must go north or you won't be able to tick off the District line at all. Indeed your second leg from Waterloo must be the District line.

Assuming you take the Northern line option from Bank, from Waterloo you have the Bakerloo, Central, District, Jubilee, Piccadilly and Victoria lines to tick off.

If you take the Jubilee from Waterloo to Westminster, that must be followed by the District to Embankment, then the Bakerloo to Charing Cross, and you're stuck with the Central, Piccadilly and Victoria left.

If you take the Bakerloo from Waterloo to Embankment, that must be followed by the District to Westminster and the Jubilee to Green Park, leaving the Central, Piccadilly and Victoria to tick off. Taking the Piccadilly to Piccadilly Circus would leave you stuck. Taking the Victoria to Oxford Circus, then the Central would leave you with the Piccadilly left, but that can be added on to King's Cross St. Pancras at the other end. So...

Route #1 = Russell Square or Caledonian Road (Piccadilly) King's Cross St. Pancras (Circle / Hammersmith & City / Metropolitan) Moorgate (Northern) Bank (Waterloo & City) Waterloo (Bakerloo) Embankment (District) Westminster (Jubilee) Green Park (Victoria) Oxford Circus (Central) Bond Street or Tottenham Court Road

Assuming you take the Central line option from Bank, from Waterloo you have the Bakerloo, District, Jubilee, Northern, Piccadilly and Victoria lines to tick off.

If you take the Bakerloo from Waterloo to Embankment, that must be followed by the District to Westminster and the Jubilee to Green Park, leaving the Northern, Piccadilly and Victoria to tick off. Taking the Piccadilly to Piccadilly Circus would leave you stuck with the Northern and Victoria left. Taking the Victoria to Oxford Circus would leave you stuck with the Northern and Piccadilly left.

If you take the Jubilee from Waterloo to Westminster, that must be followed by the District to Embankment, leaving the Bakerloo, Northern, Piccadilly and Victoria to tick off. Taking the Bakerloo to Charing Cross, Northern to Leicester Square and Piccadilly to Piccadilly Circus would leave you stuck with the Victoria left. Taking the Northern to Charing Cross, Bakerloo to Piccadilly Circus, Piccadilly to Green Park and Victoria...

Route #2 = Farringdon (Circle / Hammersmith & City / Metropolitan) Liverpool Street (Central) Bank (Waterloo & City) Waterloo (Jubilee) Westminster (District) Embankment (Northern) Charing Cross (Bakerloo) Piccadilly Circus (Piccadilly) Green Park (Victoria) Oxford Circus or Victoria

If you take the Northern to Embankment, that must be followed by the District to Westminster and the Jubilee to Green Park, leaving the Bakerloo, Piccadilly and Victoria to tick off. This give you two more routes...

Route #3 = Farringdon (Circle / Hammersmith & City / Metropolitan) Liverpool Street (Central) Bank (Waterloo & City) Waterloo (Northern) Embankment (District) Westminster (Jubilee) Green Park (Piccadilly) Piccadilly Circus (Bakerloo) Oxford Circus (Victoria) Warren Street or Green Park

Route #4 = Farringdon (Circle / Hammersmith & City / Metropolitan) Liverpool Street (Central) Bank (Waterloo & City) Waterloo (Northern) Embankment (District) Westminster (Jubilee) Green Park (Victoria) Oxford Circus (Bakerloo) Piccadilly Circus (Piccadilly) Green Park or Leicester Square

So now the question is, "Which route is fastest?"

Let's start by looking at the timetable for the Circle / Hammersmith & City / Metropolitan combination. I'm looking at the eastbound/clockwise timetables, because starting at that end means you can wait for trains of the three separate lines arriving in order. If you leave this part to the end, you could arrive at Liverpool Street or Moorgate and find the three lines are out of sequence.

Looking at the timetables leaving Farringdon on a weekday: Circle line trains are every 10 minutes at #9 minutes past the hour; Hammersmith & City line trains are every 10 minutes at #5 minutes past the hour; Metropolitan line trains are every 5 minutes at #2 and #7 minutes past the hour. The pattern is #2 Metropolitan, #5 Hammersmith & City, #7 Metropolitan; #9 Circle, so if you can be at Farringdon at #5 or #9 minutes past the hour, the next three trains should be different. From King's Cross St. Pancras the pattern is #1 Hammersmith & City, #3 Metropolitan, #6 Circle, #8 Metropolitan.

For each route I looked up the timetabled running time to catch the first Circle / Hammersmith & City / Metropolitan sequence after 12 noon on a weekday...
  1. Route 2 (26 minutes)
  2. Route 4 (30 minutes)
  3. Route 3 (30 minutes)
  4. Route 1 (32 minutes)
The times in the timetables are departure times, and I allowed zero minute interchanges which would mean your next train is due to leave at the same time as the train you just got off, giving you just the time that the train is stationary to change platforms. The 26 minute time for route 2 has six zero minute interchanges including four in a row! So, I also looked up the times allowing at least one minute for interchanges...
  1. Route 4 (42 minutes)
  2. Route 3 (42 minutes)
  3. Route 2 (43 minutes)
  4. Route 1 (46 minutes)
All of which would mean you have no chance of breaking the record! So you need to be very lucky or very fast with your changes. If I average the zero and one minute interchange times...
  1. Route 2 (34 1/2 minutes)
  2. Route 3 (36 minutes)
  3. Route 4 (36 minutes)
  4. Route 1 (39 minutes)
Personally I would first eliminate Route 1 as it is the slowest in each list and for the inconvenience of not starting at Farringdon. With Route 1 you can head to King's Cross St. Pancras planning and hoping for the right Circle / Hammersmith & City / Metropolitan sequence, but with no certainty. With the other routes you can wait at Farringdon for the right sequence, and change routes along the way if necessary.

Next I would eliminate Route 2 as it is the only one to involve changing at Charing Cross. Because it was once two separate stations, it is a long way between the two sets of platforms. And the fastest time would require a zero minute interchange there.

For the last two, changing at Green Park is the deciding factor. Route 4 involves changing from the Jubilee to the Victoria line which is the most bearable of the three combinations of change there.

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