I just came to 「交番」（こうばん） in my lessons, and the mnemonics said:
I have no idea how this one works, admittedly.
You mix a number in a series and you get a police box.
A police box?
I remember watching a variety TV program once in Japan where they asked this of the guests, and they were all stumped. At the time, all I could gather from the explanation was that the current name was short for something else that I couldn’t understand. But it turns out it comes from the combination of 「交替」（こうたい）, meaning “taking turns”, and 「立番」（たちばん）, meaning “stand watch”.
So 「交番」 comes from 「交替で番をする所」（こうたいでばんをするところ）, or “the place for standing watch in rotation”.
(Incidentally, the Japanese Wikipedia gives the readnig 「りつばん」 for 「立番」, but everything else seems to say it’s 「たちばん」. What gives?)
Source: http://police.macanow.com/trivia/trivia01.html, which I guess counts as a “Japanese Resource”