Dan Thomasson
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Knight's Tour Golden Star

While making designs on the chessboard with two mini-knight's tour closed circuits, I realized I could construct a complete open knight's tour covering all 64 squares with one circuit that also makes a four-pointed star in the middle of the tour.  Check out the following steps I used in making this knight's tour.

Step 1:

I first made a mini-knight's tour consisting of 32 moves, copied it, then rotated it 90 degrees right to make the second mini-knight's tour.
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Step 2:

I combined the previous two mini-knight's tours of 32 moves each on one board that ended up making a very nice geometric and symmetrical pattern.
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Step 3:

In the following image, I added or replaced the following knight moves with red, orange and black.
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Step 4:

In this step, I moved the red line over the top of the orange line, deleted the black line then recolored all the lines in the tour back to blue.  This made a single open knight's tour circuit.
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Step 5:

I noticed a four-pointed star shape in the middle of the tour and made the following golden star.  I changed the background to black and colored all the lines gold to match the star.  The first image shows the star with two mini-knight's tour circuits while the second image is a single open knight's tour circuit.
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Step 6:

There are many other knight's tours that have the same four-pointed star shape in the middle of their tours.  Here are just a few of them.  The first one has four mini-knight's tour circuits, the next three have two mini-knight's tour circuits while the last one has one closed knight's tour circuit.
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