The obvious solution would be to not provide access to the even-numbered answers to anyone. Students in poor countries would presumably be able to study with just the odd numbered questions (after all, university students are expected to do so). Requests from instructors could be answered with "If you can't solve these problems yourself, you have no business assigning them as homework.", or, if you're feeling particularly Kafkaesque, assume the're all actually students and congratulate them on having a particularly convincing return address, but no, you're still not going to help them cheat.
This does call for a rather more misanthropic attitude than you seem to have, though.
This does call for a rather more misanthropic attitude than you seem to have, though.