Dan Thomasson
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Knight's Tour Open Circuit V

While making designs on the chessboard with four mini-knight's tour open circuits, I realized I could construct a complete semi-magic knight's tour covering all 64 squares with one circuit.  Check out the following steps I used in making the knight's tour.

Step 1:

I first made one complete circuit consisting of 16 moves in blue then copied the circuit and flipped it vertically to make the second circuit and colored the moves red.
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Step 2:

I then flipped the first two circuits horizontally and colored the moves green and orange respectively.
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Here are the same four 16-move mini-knight tours in blue, red, green and orange.
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Step 3:

I combined all four mini-knight's tours on one board that ended up making a very nice geometric and symmetrical pattern.  The next image shows the same pattern with two closed 32 knight-move circuits.
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Step 4:

After combining all four mini-knight's tours, I wanted to keep most of the symmetrical pattern but make a single 64 move knight's tour.  I was able to do this by moving only one line (knight move) and deleting one line.  In the following image, I colored all the moves blue.  Next, I added red, orange, and black lines.
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Step 5:

In this step, I moved the red line over the top of the orange line, and deleted the black line then recolored all the lines in the tour back to blue. 
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