OTOH, if you can acheive it /with/ an Re/Im bifurcation, then it's been proved that a true real-only analogue move to the bifurcated move does exist - if only it can be found. Which is the most tantalising thing about this puzzle. Theorists are almost certain it /can/ be solved rigorously, but no-one has ever been able to prove it.

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