There's even a silly bit of Australia that has a TZ on a 45-minute boundary (UTC+8:45). Eucla is a tiny place in the middle of nowhere, population 86 in the town, though I don't know how many others might be in that TZ.
If I recall correctly from the last time I had to deal with this, it's the first 3 towns on the Eyre highway in WA coming from the SA border. This[1] suggests there are actually 4.
Well that makes sense in the real-world; Broken Hill gets South Australian television and radio and is much closer to Adelaide than Sydney (500km to 1200km), it makes sense to be on ACST not AEST
Border Village, a roadhouse on the other side of the WA/SA border, also observes Central Western Time Zone. However, the next stop on the Eyre Highway does not.
http://en.wikipedia.org/wiki/Eucla,_Western_Australia#Time_z...