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How many moves can a horse make on a chessboard?

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6  
You mean the knight? I'm really unclear as to what this means. –  Qiaochu Yuan Nov 26 '10 at 17:34
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@Nuno: I didn't downvote, but the question is very vague. I hope you agree. Please don't "pity" upvote questions like these. In effect a bad question asker gets + rep, while people who are willing to lose rep (by downvoting) to make the question better have just lost rep for nothing. –  Aryabhata Nov 27 '10 at 0:31
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@Moron: I agree that it is a bit vague. But none of the downvoters pointed this. The only complaint, made by Qiaochu, was that it's unclear what 'a horse' means. This is plausible to me, since the names of chess pieces vary from language to language. But it doesn't justify, in my opinion, the downvotes. If the question isn't clear, it's polite to ask for clarifications, as Qiaochu did. Also, I didn't "pity" upvote this question. The tag graph-theory suggests what is being asked here. And for me it's not a stupid/uninteresting question. –  Nuno Nov 27 '10 at 0:55
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@Nuno: I believe both of Qiaochu's statements were independent, and in fact his second statement points out that the question is unclear. Given that, it is completely reasonable that others didn't repeat what Qiaochu said (and hence the absence of explanations of downvotes). I have to disagree that the tag graph-theory (which is interesting to me too) suggests what the question might be. It is still very unclear. "How many moves can the knight make?" is really too vague, even keeping the graph-theory tag in mind. Posting a question which is not clear is rude to the answerers... –  Aryabhata Nov 27 '10 at 3:11
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... especially when this is taken from a homework, where the question must have been clearly specified to the OP. All that was needed is to translate it verbatim. Also, the OP never made any attempt to clarify the question, inspite of Qiaochu's comment and subsequent downvotes. –  Aryabhata Nov 27 '10 at 3:27

2 Answers 2

See, the knight's graph on wikipedia. It comes with the following graph; the vertices are marked with the number of legal moves of a knight from that location.

alt text

If you want to know the total number of moves that a single knight could theoretically make, then you can sum these numbers:

\[16 \times 8 + 16 \times 6 + 20 \times 4 + 8 \times 3 + 4 \times 2=336\]

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That piece can move in an L-shape. So potential, it can move in 1 of 4 directions (unless it's restricted by one edges of the board).

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4  
Uh, eight surely? That is to say, an unrestricted knight has a choice of eight squares. –  Oscar Cunningham Nov 26 '10 at 21:06
    

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