London Underground puzzle

A few days ago I posted the following puzzle to my Google+ stream:

Can you find a route around the London Underground map taking in exactly one stop on each line (including DLR and Overground)? That is, get on the tube at one station, go one stop, change to another line, lather, rinse, repeat until you’ve been on every line.

London Underground map

I teased that I had a solution but I wanted to give people some time to work on their own solutions before describing my own. If you feel like giving it a shot, stop reading now. I’m about to describe how I went about finding a solution.

I started by recognising that any path between two stations that had only a single line but more than one leg could not be part of the solution. For example, the (direct) journey from Baker Street to Oxford Circus uses only the Bakerloo line but takes in an extra stop at Regent’s Park along the way, so it can’t be used if we’re to travel only one stop on each line.

There’s a bit more flexibility for a route that’s covered by more than one line. For example you would be allowed to travel from South Kensington to Victoria via Sloane Square by using the Circle line for one leg and the District line for the other. But you’re limited here to journeys of no more than two stops along these lines. Similarly, you can go three stops along the short route served by the Metropolitan, Circle and Hammersmith & City lines.

So I took the standard Tube map (above) and opened it in a graphics editor, and just started erasing pieces that couldn’t possibly form part of the solution. I left only stations that are served by more than one line, and which are connected directly (over a single-leg journey) to other stations served by more than one line.

Actually this approach removes some stations that could still potentially form part of a solution, because the two stations at the start and end of your route don’t need to be served by more than one line. It would be a simple matter to add those stations back at the end if it turned out to be necessary (though in fact it doesn’t).

Once I had my trimmed down map it was very easy to see that there would be a pretty even split with about half of the lines being west of the Waterloo & City line and half being east. The Waterloo & City line was really what made this a tractable problem, because it forces you to use Bank and Waterloo stations in any solution.

I spent a bit of time convincing myself it was impossible to get from the Metropolitan or Hammersmith & City lines down to Waterloo (via either Kings Cross or Baker Street), so those had to be on the east side of the solution. Victoria, Piccadilly and Bakerloo were all obviously on the west. The DLR could only ever have been on the east side, as could the Overground. The Jubilee looked unlikely to fit on the east. The Central, Circle, District and Northern lines were a bit more ambiguous, but it’s quite easy to show that you can’t get from Waterloo to the Piccadilly line without using at least two of Northern, Circle or District.

That reduced the field enough to just try out a few variations. The route I finally came up with was:

London Underground puzzle solution

  • Start at Moorgate
  • Take the Metropolitan line to Liverpool Street
  • Take the Hammersmith & City line to Aldgate East
  • Take the District line to Whitechapel
  • Take the Overground to Shadwell
  • Take the DLR to Bank
  • Take the Waterloo & City line to Waterloo
  • Take the Jubilee line to Westminster
  • Take the Circle line to Embankment
  • Take the Northern line to Charing Cross
  • Take the Bakerloo line to Piccadilly Circus
  • Take the Piccadilly line to Green Park
  • Take the Victoria line to Oxford Circus
  • Take the Central line to Bond Street

Of course you could substitute Aldgate for Moorgate and/or Tottenham Court Road for Bond Street, or do the whole thing in reverse. Aside from those variations, I think this is the only possible solution, though I haven’t proved it.

The gamification of football

Part of my ongoing, half-assed attempt to get myself into shape involves playing indoor football every week with some of my colleagues.

We aim to have five people per team, but we rarely hit that number. Sometimes we play an exhausting three-a-side game. We once played seven-on-seven, which was like trying to move a ball around a crowded nightclub. Often one team will be bigger than the other.

All in all it’s a pretty non-competitive event. We don’t make much of an effort to keep track of the score, and even when we do we’re still very likely to give up on scorekeeping at the end and just declare “last goal wins” when we’re about to run out of time.

Our relaxed approach to the game means that we’re more likely to try a manouvre that might look cool—like a bicycle kick or a diving header—than to do something that will actually lead to scoring a goal.

Chatting after the game today we came up with the idea of ‘gamifying’ the game. Just like many parts of life are being ‘gamified’ these days—like unlocking points and badges for visiting certain places in Foursquare—you can imagine getting achievements for things that you do in a real football game.

Some badge ideas:

  • Head boy: Score with a header. This is the achievement I spent most of today’s match trying (and failing) to unlock.
  • BFFs: Set up the same player for a goal, or have them set you up for a goal, 3 times in a match.
  • Poultry farmer: Be on the receiving end of a foul. (Is that too bad a pun?)
  • Postman: Hit the post 5 times in a match.
  • Greg Louganis: Take a dive!

Any other ideas?

The next step is to write the image recognition software to analyze video footage of a match and assign achievements (thereby earning the ‘Spent altogether too much time on such a silly idea’ badge).

Being Wrong

I enjoyed this paragraph from Tim Harford’s Financial Times piece on the reasons for, and consequences of, politicians’ love of certitude:

It is not clear why we enjoy certitude so much – certitude being the subjective experience of feeling certain. In contrast – as Kathryn Schulz observes in her wonderful book Being Wrong – there is simply no psychological experience of “being wrong” at all, only the lurching realisation of having been wrong until a moment ago.

I’ve never been a huge fan of being wrong. Now I can claim that I’ve never experienced it.


Amazon search result: Club Orange Soft Drink Pack of 8 2 Litre Bottles Buy new: £34.99 (£2.19/l)I’ve finally found a way to make England habitable.

I’ve always been bewildered yet faintly impressed that the rest of the world can survive with Fanta as its primary, and often only, carbonated fruit drink. I don’t think I need to point out to people who have tasted it that Fanta is the juice of Nazis.

Seven Years On

While we’re still celebrating milestones, I have one of my own. I started this blog seven years ago, on January 7, 2003. Back then it was made of hand-coded HTML that lived on the servers of my university’s Internet Society.

I soon moved it to a self-made blogging platform on those same servers. From there it moved to a professional web host, on yet another custom blogging platform, and with its own domain. Most recently it moved to a new domain, and I finally gave up on maintaining my own software and migrated all the content to WordPress.

I’m quite happy that through all those software changes and server moves I still have every post I’ve ever written for this blog, right back to the very first one.

That first post was about the result of a little Web quiz that took details of my physical fitness, intelligence, education, and lifestyle and, through the twin magics of mathematics and making shit up, informed me that I was worth exactly $2,320,314. I would have hoped my organs alone could fetch that much or more, but I’m not the expert here.

Looking back on my first post I decided to see if that quiz was still online and, more importantly, if my value had changed at all. You’ll be delighted to hear that not only is the quiz still happily digesting humanity into currency, but I’ve gone up in value to an amazing $3,061,316. That’s an increase of nearly 32%. Maybe that’s not the biggest possible return over seven years, but at least it’s going up.