The June Vandal Science News featured the following tricky Geography puzzler:
There is a place in the world where traveling nine miles in any direction will require you to set your watch ahead one half hour, then back one half hour, then finally ahead again one half hour (in order to keep the watch set correctly at all times). In what country is this place located?
The simple answer is that the place is located in India. More specifically, it is a very small enclave of India called Dahala Khagrabari that lies within an enclave of Bangladesh called Upanchowki that itself lies within an enclave of India called Balapara Khagrabari (that lies within Bangladesh). Add to that confusion the fact that India and Bangladesh maintain time zones separated by one half-hour, and you get the situation described by the puzzler.
See Cooch Behar district (Wikipedia) for more information, or an annotated map of Cooch Behar of this messy piece of the India / Bangladesh border.