diamond geezer

 Saturday, November 02, 2019

Today's post is about making a journey through tube stations whose names include every letter of the alphabet.

What's the shortest route which ticks off all 26 letters?

n.b. Tube stations only.
n.b. Route must pass through consecutive stations.
n.b. We're looking for the journey which passes through the fewest stations.
n.b. In case of a tie, the fewer trains the better.


For example, OVAL ticks off four different letters, KENNINGTON gets six more, but WATERLOO would only add another two. So that's not a great start.

The key to this challenge is knowing where the least frequent letters are.

In particular there's only one Z on the tube map, at BELSIZE PARK, so we're going to have to include that.



Hurrah, that's ten letters of the alphabet [ABEIKLPRSZ] sorted already.

No stations further up the Edgware branch of the Northern line have any interesting letters, so we need to head south instead.

And that forces us to go to CHALK FARM and then to CAMDEN TOWN, which it turns out is a truly excellent start.



Chalk Farm gifts us [CFHM], then Camden Town offers [DNOTW], and suddenly there are only seven letters [GJQUVXY] left to collect.

We can ignore U, because that comes for free when we collect Q, and G shouldn't be difficult to get either.

In which case the entire problem boils down to "What's the quickest way to grab J, Q, V, X and Y starting from Camden Town?"

I've knocked up a map.



• There are five X stations on the Underground (Brixton, Croxley, Oxford Circus, Uxbridge, Vauxhall), but only Oxford Circus is in the centre of town.
• There are three J stations on the Underground (St James's Park, St John's Wood and Willesden Junction), but the latter is too far out.

All my attempts at finding a best route pass through Oxford Circus, for the X, before heading on to either St John's Wood or St James's Park for the J.

It all comes down to how best to collect the Q, V and Y along the way.

• For Q, central London offers Queensway and four Something Squares.
• For V, either Covent Garden or Victoria look most promising.
• Although there are several Ys, Piccadilly Circus is the most central.

And here's what I reckon is the quickest way to complete the A-Z challenge (unless you can do better).

First the Northern line, Bank branch, south. That's 20 letters done already.
BELSIZe PARKCHalk FarM → CamDen TOWN → EUston
Then onto the Victoria line, via an easy cross platform interchange at Euston.
→ Warren Street → OXford Circus
Then to the Bakerloo line, via another easy cross platform interchange.
→ PiccadillY Circus → CharinG Cross → Embankment
And finally to the District line to pick off the final J, V and Q.
→ Westminster → St James's Park → Victoria → Sloane SQuare


This journey ticks off all 26 letters of the alphabet in 13 stations via four trains. I think that's unbeatable.

And, having tried it, it took 27 minutes. If only it had been 26.

Update: No, Chris can do it quicker, in just 12 stations! (but on seven trains, so slower)

BELSIZe PARKCHalk FarM → CamDen TOWN → EUston → Warren Street → OXford Circus → Tottenham Court Road → Leicester SQuare → PiccadillY Circus → Green Park Victoria → St James's Park


I then noticed that five of the stations I'd passed through hadn't contributed anything. If you take out Chalk Farm, Camden Town, Euston, Warren Street and Embankment, the other eight stations still contain all the letters of the alphabet between them.

BELSIZe PARK →→ OXForD CircUs → PiccadillY Circus → CHariNG Cross →→ WesTMinster → St James's Park → Victoria → Sloane SQuare

So here's my challenge for you. What's the fewest number of tube stations required so that every letter of the alphabet appears at least once? The stations don't have to be adjacent, they can be anywhere on the network.

Eight is beatable. Can you do it in seven, or six, or even five?

Update: Ian's done it in six.

[BELSIZe PARK, FUlHaM BrOaDWaY, QueeNsway, RodinG Valley, VauXhall, Willesden JunCTion]

Update: That used 71 letters, but Ian's second attempt only needs 59.

[BELSIZe PARK, BOroUGH, OXForD Circus, QueeNsWaY, ST JaMes's Park, Vauxhall]

Update: Swapping Vauxhall for Oval cuts this to 55 letters.

[BELSIZe PARK, BOroUGH, OVal, OXForD Circus, QueeNsWaY, ST JaMes's Park]

Update: Two readers, the wub and zin92, have slimmed it down to 52 letters.

[BELSIZe PARK, CHalk FarM, OVal, QUeeNsWaY, ST John's WooD, UXbridGe]



We're fairly certain six stations and 52 letters is the fewest possible. Thanks!

(but it used to be possible in five)


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