TITLE: "Simple" beautiful math proof
QUESTION [95 upvotes]: Is there a "simple" mathematical proof that is fully understandable by a 1st year university student that impressed you because it is beautiful?

REPLY [2 votes]: Can a Chess Knight starting at any corner then move to touch every space on the board exactly once, ending in the opposite corner?
The solution turns out to be childishly simple. Every time the Knight moves (up two, over one), it will hop from a black space to a white space, or vice versa. Assuming the Knight starts on a black corner of the board, it will need to touch 63 other squares, 32 white and 31 black. To touch all of the squares, it would need to end on a white square, but the opposite corner is also black, making it impossible.