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### Solutions for Act I Scene 4 - ASTC

Initially, this puzzle presents us with a series of coloured lines and numbers. Since this information alone doesn't tend to suggest the initial direction of our puzzle, it is probably a good idea to turn our attention to the title.

Most puzzlers would hopefully have come across the ASTC acronym in high-school mathematics, where it was used to remember the signs of trigonmetric functions in the 4 quadrants of the number plane. Whilst this might seem like a promising lead at first, it is quite difficult to even begin to apply trigonometric analysis to our puzzle, which should suggest that this approach is not the intended one. Instead, the title is meant to hint at the common mnemonic used to remember the letters ASTC, All Stations To Central.

Following this realisation, it should be clear that the diagrams are representing train lines. If we're looking to find these train lines somewhere on a real map, and since this is the Sydney University puzzle hunt, the first rail system to consider should be that of suburban Sydney. A network map for this system can be found on the Sydney Trains website.

Using the colours and curvatures of the tracks provided, as well as the small lines at the ends of each track, we can begin to determine which train lines are being represented in our 11 diagrams, with the initial assumption that our trains all travel to Central. Whilst this is possible for several of the diagrams, it quickly becomes clear that not all the lines can start or end at Central. For example, the last (light blue) track extends horizontally to the left, which when looking at the rail map clearly does not happen when travelling from Central.

The jump here is to realise that, as clued in the final hint, the title is deliberately in acronym form in order to allow for the final C to represent any station beginning with C. For example, the final light blue line ends at Cronulla rather than Central. After figuring out which train lines each diagram is corresponding to, the only information we are yet to use are the numbers attached to each line.

The natural step from here is to determine the station which is the corresponding number of stops away from our end station. In doing so, we retrieve the following list:

Wolli Creek - Central
Milsons Point - Central
Waitara - Chatswood
Ingleburn - Cabramatta
Sutherland - Cronulla
Toongabbie - Clyde
Burwood - Central
Circular Quay - Central
Clyde - Carlingford
Seven Hills - Clyde
Jannali - Cronulla

Indexing into the station names does not give any recognisable words or phrases, and so at this point we must look for another way to decrypt letters from our situation. The final leap of the puzzle is to realise that, as hinted by the To in All Stations To Central, we need to focus on the journey from one station to the other, rather than the stations themselves. In fact, all the stations lie relatively close together along their respective lines, suggesting that the durations of the journeys between them do not take long.

It turns out that if we investigate the official timetable on the same website as our map, all the journeys depicted in our puzzle take no more than 26 minutes. (A "timetable-like" figure was included in the background of the puzzle to confirm that this is the correct way to determine the journey times).

So after determining how long it takes for an all stops service to perform each journey, we can retrieve our final thematic message.

JourneyTimeLetter
Wolli Creek - Central16P
Milsons Point - Central12L
Waitara - Chatswood21U
Ingleburn - Cabramatta19S
Sutherland - Cronulla15O
Toongabbie - Clyde18R
Burwood - Central13M
Circular Quay - Central9I
Clyde - Carlingford14N
Seven Hills - Clyde21U
Jannali - Cronulla19S