knight's tour exercise

I was looking for 'brain training' on the interwebs in my copious amounts of leisure time, and here is this exercise that lets you see if you can figure out how a knight hops to every square on the board.  I've never solved it before. I saw a diagram once about it but I failed to memorize it.  It seems really nice for maybe getting my brain to comprehend knight movements a little better.  When I do it now I am failing by a lot so far.  I've tried it about 10 times without trying extremely hard and I get stuck in the 50s typically.  maximum about 56 i think.
http://www.brainmetrix.com/chess-knight/
I have javascript blocker addon and I can see it has very few ads or blockers it uses!

I've seen this exercise before, it is indeed difficult!

Using a strategy of always moving so as to keep near the edge of the board and thereby leaving just the middle, I am a bit careless at the end and get 65 (same on 3 occasions). I think you could probably do it with this approach but with more carefully calculating the end once it gets dangerously close (the first part, clearing about 75% of the board and leaving a single roughly symmetrical block is easy, and it seems plausible it is possible to complete it).

1st try 74

2nd try 71

3rd try 67

4th try 69

5th try 68

I wonder how many solutions there are?

Don't know, but I think I recall this has been calculated.