I enjoyed this puzzle. I was not able to solve it before looking at the answer, but others may be able to. I will give hints if there is interest. I read the puzzle in **Mathematical Puzzles: A Connoisseur’s Collection ** by by Peter Winkler. Despite the title, there is a chapter on Geography.
(This puzzle refers to the United States)
A telephone call is made from an East Coast state to a West Coast state, but it is the same time in both places. How is this possible?
I think it would be from those parts of Alaska that lie beyond the International Date Line to the main part of Alaska. Those the other side of the IDL would be technically the easternmost points in the US, hence an East Coast state while the rest of Alaska is a West Coast state.
A piece of Florida (Central Time) and a piece of Oregon (Mountain Time) have the same time for one hour each year, at the end of Daylight Saving Time. The piece of Florida goes from 2 AM back to 1 AM while the piece of Oregon has not technically fallen back an hour yet. Thus from 1 AM to 2 AM it is the same time in both time zones.