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12

First things first: let's check the divisibility. There are 64 squares, and the knight is standing in one of them. That leaves 63 squares to cover, and each move covers 3 squares, so that seems to work out. That means, however, that we won't be able to create a closed loop, so every solution we find only solves the puzzle for the starting point and, by ...

24

I have a computer program for solving packing problems, and found a way to use it to solve this problem. One of the solutions it found is below: Note that this is very close to the attempted solution in the question, as it differs only in the top left quadrant. Modelling the problem in this way will not find all solutions (I'd need to allow other tile ...

1

I love this puzzle! And here is a quick albeit very mathy solution: Let $\mathcal{B}$ be the canonical basis of $\mathbb{Z}_2^{8 \times 8}$ then there is a surjective linear map $\varphi : ~\mathbb{Z}_2^{8 \times 8} \rightarrow \mathbb{Z}_2^6$ with $\varphi(\mathcal{B}) = \mathbb{Z}_2^6$. This is due to a standart result in linear algebra. A linear map \$ \...

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