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I needed to get from Riga to Bucaresti. I had trains connecting Riga to Kyiv, but the route from Kyiv to Bucaresti was taken by another player. I played a station on Kyiv, but the route did not complete (I'm playing the iPhone version).
What am I misunderstanding about the use of stations?
A Train Station allows its owner to use one, and only one, of the routes belonging to another player, into (or out of) that city to help him connect the cities on his Destination Tickets.
As per the instructions (emphasis mine), a station can only be used on a single route into or out of the city on which it's placed. Even if the route from Riga to Kyiv was complete (and I'll assume you double-checked that), the Kyiv station could not be used to complete the ticket if it was already being used to connect a different route (i.e. via Kyiv-Warszawa, Kyiv-Smolensk, Kyiv-Wilno, Kyiv-Kharkov or Kyiv-Budapest).
If the Kyiv station was already prescribed to a different route, you could still complete the ticket by activating the Kyiv-Bucaresti line through a station placed on Bucaresti instead.
As for the electronic version of the game, it does not immediately show tickets as complete if they rely on stations; since only one of the routes out of any given city can be used, and which route that may be is not decided until after the game is over (but before the score is calculated), the game doesn't know which route you want to use until the end of the game. It will give you credit for routes completed with properly-used stations when it tallies up your score at the end.
The station, when played, only works for one chunk of track. In the boardgame version, players usually move the station physically over the track being used, thus helping to visualize the "one, and only one"...
Note that, page 6 of the rules for TTR:Europe, the following:
If a player uses the same Station to help connect cities on several different Tickets, he must use the same route into the city with the Station for all of those Tickets. The Train Station owner does not need to decide which route he will use until the end of the game.
(Emphasis mine.)
So, in the case of the OP's issue, obviously, another route was used (probably for other tickets).
Having played both the computer version and the tabletop version, however, occasionally the computer version glitches on stations, using it for the lower value route.
