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# Cole D. Pruitt

• @Alex #38 So Puzzle 12 would be $$\lfloor\frac{n}{2}\rfloor$$ and Puzzle 13 would be $$\lfloor\frac{n+1}{2}\rfloor$$. Am I crazy? I get a different form of the answer to Puzzle 13: $$g(n) = \lceil \frac{n}{2} \rceil$$. But $$\lfloor \frac{n+1… • I'm afraid I'm still confused about the answers to puzzles 12 and 13 that are re-quoted here in the lecture material - I get a right adjoint \(g(n) = \lfloor n/2 \rfloor$$, not $$\lceil n/2 \rceil$$ as is given in the lecture. Or (much less likely…
• Dan, I agree: as far as I can tell, it hinges on the compelled move question with respect to the only non-reversible piece (pawn), and/or whether 0 legal moves is included in the definition of $$\leq$$. I think if pawns are all removed from the boar…
• How about the set of all legal chess positions as a preorder? In this case, $$\leq$$ is interpreted as "can produce by legal moves". This doesn't seem partially ordered, though, because cycles are possible: I can move a bishop back and forth to rep…