I used to have 2 routs memorized 2 or so years ago, and used one of them as an avatar. I'll need to see if I can find that image from the office Monday or so.
This is a great little challenge to show a friend when you meet them for some OTB.
I did 71 and 70 on my first two tries. Then I threw in the towel and learned the opensolution that was posted above (in the link provided by zoot). I think it would be more worthwhile to learn the closed solution, because then you could do it from any start square. That would be much more impressive to show off!
George Koltanowski, did his "Knights Tour" Blindfolded, that is on a large Chess board he would write in various names, i.e. a1=Spassky b3=Fischer a5= 8 diget number and so forth. George would study the board for a few minutes and turn his back to the board and ask a viewer to place the Knight anywhere on the board, again without looking George would recite what was on the square and where the Knight should move too, reciting what was on that square, NEVER landing on the same square twice and remembering all that was placed on the board.. George was remarkable, as a chess player and Ambassdor to the Chess world.
Posted by davutuysal on chess.com Start with any random square for the knight.Write down all possible 2nd moves.To choose the 2nd move,select the one that leads to a minimum count on the third move.Repeat until complete.