The internet is filled with things. Here are some of them.
Odd numbers were considered masculine; even numbers feminine because they are weaker than the odd. When divided they have, unlike the odd, nothing in the center. Further, the odds are the master, because odd + even always give odd. And two evens can never produce an odd, while two odds produce an even. Since the birth of a son was considered more fortunate than birth of a daughter, odd numbers became associated with good luck.
This time zone is an obnoxious UTC+8:45 (yes, really) and covers a tiny and nearly-uninhabited strip along Western Australia's southeastern-most coast. But not entirely uninhabited, clearly, or else why exist? So for these few hundred people, they live in a world where their clocks are 15 minutes off the hour.
Perhaps this is less a weird time zone, and more a community staunchly holding out against the idea of time zones in the first place, back when each community set their own local noon and inter-state commerce just happened when it happened.