The first step in this puzzle is to study the fully worked DEMO puzzle and determine the rules. The puzzle is solved in four distinct stages:

1. Using just the numbered circles (islands) and their placement in the grid, solve a Hashiwokakero puzzle. Each island is connected to others by bridges which run only horizontally and vertically, at most 2 between each pair of islands, never intersecting, and such that each island is served by the number of bridges indicated by the number printed on it.
2. In the solution, assign each bridge a color. For single bridges, the color is determined by XORing the colors of the connected islands, using light mixing rules. For double bridges, one bridge is the color of each island.
3. Now use the resulting set of colored bridges as the map for a game of Ticket to Ride. The islands don't have names, but the small maps next to each player are the tickets and show the routes pictorially. Each player has the train cards necessary to buy their track segments.
4. Extract a message by following the routes in the order they are given across all four players. The tickets have arrows indicating the direction to read. From each track segment used which is N segments long, extract the Nth letter from the color of the segment. Each ticket's route provides one word. (In the demo puzzle, the route spells DEMO. It's DEMO instead of SAMPLE or EXAMPLE because the colors don't provide the letters for those words!) Then solve the clue you get.

Hashi and Bridge Coloring

The solutions to the first two steps, solving the Hashiwokakero and coloring the bridges, are depicted below.

Ticket to Ride

Note that in this version of the game, as promised, it is an extra-hard one for the players, since there are no colorless tracks or rainbow train cards. In addition, somebody has replaced the orange train cards/segments with cyan ones.

Some players have multiple ways to connect all their routes, but there is only one way for all the players to connect all their routes, and the players have just enough train cards to do it. Player 1's routes are forced without any knowledge of what the other players are doing, so that is a good place to start.

In this grid, the track segments are labeled for which player took each one. There are some segments not claimed, some of which are present in order to make the hashi solution unique, some of which are there in order to make the colors necessary for extraction, and some of which are just there to make the puzzle tougher.

Extraction

Read along the routes necessary to satisfy the nine tickets in the order they are given, in the direction of the arrow on each one. The grid dots, which usually aren't given for Hashiwokakero, are given here to help you measure distances, since the letter to extract from each segment is the length of the segment indexed into the name of the color of that segment, as printed on the train cards.

• BLU(E), WH(I)TE, MA(G)ENTA, W(H)ITE, MAGEN(T)A = EIGHT
• B(L)ACK, WHIT(E), WHI(T)E, MAGEN(T)A, GR(E)EN, G(R)EEN = LETTER
• B(L)UE, YELL(O)W, BLA(C)K, BL(A)CK, WHI(T)E, WH(I)TE, YELL(O)W, CYA(N) = LOCATION
• YELLO(W), WH(I)TE, WHI(T)E, W(H)ITE = WITH
• (M)AGENTA, BL(U)E, BLA(C)K, W(H)ITE = MUCH
• WHI(T)E, G(R)EEN, CY(A)N, WH(I)TE, MAGE(N)TA = TRAIN
• WHI(T)E, G(R)EEN, CY(A)N, BLA(C)K, BLAC(K) = TRACK
• CY(A)N, CYA(N), RE(D) = AND
• YEL(L)OW, YELL(O)W, CY(A)N, RE(D), WH(I)TE, MAGE(N)TA, (G)REEN = LOADING

So the full clue is EIGHT LETTER LOCATION WITH MUCH TRAIN TRACK AND LOADING. This clues the answer RAILYARD.