A Knight's move is as in chess, an L shaped move, 2 squares in one direction and 1 square in the other direction.)

A Knight's Tour is one where the knight passes through each square exactly once.

You may start on any square you wish.

* For extra credit, come up with a re-entrant tour: at the end, the knight is exactly one knight's move away from the starting square.

* For EXTRA extra credit, make sure that the path is, in some way, symmetrical.
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Since "Knight's Tour" is a term used outside the scope of this problem, I'm sure you can find an answer on the internet. Please find an independent solution.

This does not require a computer program.

This solution isn't symmetrical, but it is a re-entrant tour.

A1 - B3 - D4 - B5 - C7 - A8 - B6 - D7 - E5 - G4 - F2 - H1 - G3 - E2 - C1 - A2 - B4 - D3 - C5 - A6 - B8 - C6 - A7 - C8 - D6 - E8 - G7 - H5 - F4 - H3 - G1 - F3 - H2 - F1 - E3 - D1 - B2 - A4 - C3 - D5 - E7 - G6 - H8 - F7 - G5 - E4 - D2 - B1 - A3 - C4 - A5 - B7 - D8 - 36 - F8 - H7 - F6 - G8 - H6 - F5 - H4 - G2 - E1 - C2 - A1

For my method, I actually took out a chess set and took 4 paths that went 3 quarters around the board and didn't overlap and connected them all in the upper-left corner.