I found it amusing to learn about the Australian time zones: Australia is basically divided into three parts, which could be very nicely +8, +9 and +10, except it is +8, +9:30 and +10. OK. Except that in the south, two of the three zones are split and do DST, which the north does not do, so you get +8, +10:30 and +11 in summer in the south (but the north keeps +8, +9:30 and +10).

Now, that was my amusement for a couple of years.

Then I learned that there is Broken Hill, which follows a time zone different from the surrounding area because of the train track history. And there is Lord Howe Islands, which uses a +0:30 minute DST shift instead of an hour.

And then I learned that history also experimented with 20 minute and 15 minute DST shifts, and that double DST (or Hochsommerzeit in Germany) was quite common, too.

You can probably go on and on and on as you dig deeper, and at some point, anyone's mind will blow, I guess.