"Can you teach me to play mahjong?"
Why does this sentence use 能？I would think it should be 可以.
1) I guess, with 能 the sentence means "Are you able to teach me mahjong?" which is essentially asking if that person knows how to play mahjong (and therefore, has the ability to teach it).
2) I guess with 可以 the sentence would mean "Is the situatuon such that you can teach me mahjong (do you have the time, the desire, etc)"
The thing is, with the given English translation of "Can you teach me mahjong?" I, as a native English speaker, would assume you're asking number 2 above unless the context indicates otherwise.
Personally, in about twenty years of sometimes occasional and sometimes intensive exposure to Chinese, I've never heard anyone say it with "玩", though you can find a lot of examples of it with an internet search, so it seems to be possible. But perhaps a native Chinese speaker can provide a definitive answer.