Knight's Tours

Besides the Eight Queens puzzle, the Knight's Tour is the other classic mathematical chess puzzle, namely, to have a chess knight complete a tour of all 64 squares, using a sequence of legal knight moves, without revisiting any of them. In this video I discuss knight's tours at length, including how many there are, including closed tours (ones that return to their starting square), on boards of various sizes, as well as how to find them.

[@davesmathchannel-ts2ik]

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[@davesmathchannel-ts2ik]

I made a small mistake at the end of this video. The last slide I showed is not quite a complete knight's tour, since a few squares haven't been visited and are unreachable, so in this case, backtracking would be required to complete it.

[@irrelevant_noob]

Also i'd argue that at 1:55 the single "tour" for n=1 isn't closed. 🧐
... and you stated as much at 3:09, considering that 1 is odd. ^^

[@davesmathchannel-ts2ik]

@@irrelevant_noob Thanks for your corrections. Good observations!