Just a thought, but running with Kilydd's L~ton hypothesis and selecting Loughton over Leyton due to its greater magnetic selectivity quotient, how about stringing and ghost/live bifurcation on (move=2), possibly involving a recent ghost like Aldwych, or maybe Epping. The live side of course would have to be very lively indeed - maybe Baker Street or Bank. The dead:live dichotomy would perhaps then allow a move to a vortex station such as Sloane Square (Dollis Hill being unusable for obvious reasons). This might then lead to (move=3) being a Magenta station, though not if Baker Street had been used in (m=1) of course, it being a Magenta itself. What d'you reckon ?

Sorry, sorry, sorry - for Epping in the above, read Ongar obviously - the latter being a ghost, the former not.

This is probably a stupid question, but I am puzzled as to why this has not been solved by brute force and appropriate computing power. By analogy, think of how the four-color (or should that be for-colour?) map conjecture was eventually proved by reducing the problem to a finite (relatively small) number of maps and then checking them all. Here, at the level of actual moves, there is only a finite (and relatively small) number of four move combinations.

I'm aware, of course, that this is a simplification, because more than the pure moves come into play: there is a large (though still finite) set of possible initial placements on the board; token loadings can take on a large (though still finite) number of values; n-furcations are possible; and there are several continuous variables to worry about, such as LV and token weightings. Still, if this four-move combination is not a measure-zero possibility, one would expect that even a crude algorithm could easily limit the search space and pin down permissible ranges for LV and token weightings.

I must be missing something, but I'm not sure what.

[CdM] Speaking only for myself; I'm too lazy to program it.

Anyway, did some more work on this today, and spotted an interesting complementary move to my Friday's suggestion.

Alperton->Kensal Green->St John's Wood->Mornington Cresent. This is just a straight horizontal. But curiously in the complex plane the sequence has five components

.. not four, because it cuts the Metropolitan line between Finchley Road and Baker Street.

Anyway, I'm still looking, though.