please empty your brain below
6.
Belsize park
Willesden junction
Roding valley
Vauxhall
Fulham Broadway
Queensway

Ian | 02.11.19 - 7:43 a.m. | #

Fewer letters

belsize park
st james park
queensway
oxford circus
borough
vauxhall

Ian | 02.11.19 - 7:58 a.m. | #

And in the style of Fermat, I could do it in five, historically.

Ian | 02.11.19 - 8:13 a.m. | #

Swap out Vauxhall for Oval to make it a bit shorter

Geheee | 02.11.19 - 8:35 a.m. | #

Unlike many such questions, this one appears to lend itself to a rapid computer solution. The total number of bags of six stations out of 270 is quite manageable, so a program could inspect every such bag, reject it if it doesn't cover the alphabet, and rank the survivors by total letter count. Indeed, someone may have done it while I've been typing this.

Malcolm | 02.11.19 - 9:03 a.m. | #

I think there might be more efficient ways, Malcolm, as there are 508 billion combinations of 6 from 270.

Ian | 02.11.19 - 9:12 a.m. | #

Sure some optimisations would help. For a start, it is really bags of 5 from 269, as DG has already pointed out that Belsize Park is compulsory.

dg writes: That only cuts the number of combinations to 11 billion. Still wildly impractical.

Malcolm | 02.11.19 - 9:38 a.m. | #

Five is possible if you allow DLR stations.

Ian | 02.11.19 - 9:51 a.m. | #

Then with only 5 X stations, the number of permutations becomes 5 times the number of 4-bags out of 268.

dg writes: Still 1 billion.

Professor Gimothy Towers | 02.11.19 - 9:52 a.m. | #

The problem can be reduced further, as the solution has to include Belsize Park, one of the three J stations, one of the five X stations, one of the seven "Q" stations and one of the twelve "V" stations. Thus 1x3x5x7x12= 1,260 combinations. (minus 20 because of double-counting Vauxhall)

timbo | 02.11.19 - 11:38 a.m. | #

Or you could just work it out yourself.

It is possible to get below 55 letters.

diamond geezer | Homepage | 02.11.19 - 12:00 p.m. | #

Using Underground stations only, six stations is the minimum, and the shortest I can find is 52 letters:
Belsize Park, St John's Wood, Uxbridge, Queensway, Chalk Farm, Oval

the wub | 02.11.19 - 1:29 p.m. | #

Agreed. Beat me to it by 4 minutes!

Regards

zin92 | 02.11.19 - 1:33 p.m. | #

Agreed! I believe that is the shortest list.

I like that it uses 26×2 letters.

Five stations is only possible if you resort to including the Overground or the DLR (or former tube stations...)

diamond geezer | Homepage | 02.11.19 - 2:00 p.m. | #

I expect DG is right that 5 is impossible. But can this be proved? Given the number of possible sets of 5 stations. Perhaps an argument among the Js, Xs and so forth, as suggested by timbo above, would do it.

Malcolm | 02.11.19 - 2:13 p.m. | #

Proof (?): none of the 1,260 combinations suggested by timbo contains all 26 letters.

Regards

zin92 | 02.11.19 - 2:51 p.m. | #

I get to five stations by adding disused station Verney Junction - replaces Oval for OV and St John’s Wood for TJ, with Uxbridge taking D. 51 letters

NLW | 02.11.19 - 10:09 p.m. | #

...which is
[BELSIZe PARK, CHalk FarM, QUeeNsWaY, UXbriDGe, Verney JuncTiOn]

diamond geezer | Homepage | 02.11.19 - 10:59 p.m. | #

My disused version is...
[BELSIZe PARK, MOorGaTe, QUeeNsWaY, VauXHall, WatForD JunCtion]
...which is also 51 letters.

diamond geezer | Homepage | 02.11.19 - 11:00 p.m. | #











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