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I have this mind puzzle which has bothered me the latest days.

QUESTION: Question

CHOOSE ANSWER: alternatives.

I realize that there are relations (rotation and translation) between three pairs of the matrices (1-4, 3-5, 6-7), but for two of them (2 and 8) I see no relation. Can anyone help me stop bothering? Which is the missing matrix and why? :)

nize
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  • Each table is a permutation of the preceding table, however there is no single permutation $p$ such that each table is $p$ of the preceding table. – Jack M Jan 25 '15 at 12:10

1 Answers1

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The transformation that takes a matrix to the one to its right is as follows: shift the columns to the right by one, wrapping around; shift the leftmost column down by one, wrapping around; then apply the symbol permutation $X \to O \to \Delta \to X$.

[Edit for clarity: The permutation on the matrix elements is $$ \left( \begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array} \right) \mapsto \left( \begin{array}{ccc} 9 & 1 & 2 \\ 3 & 4 & 5 \\ 6 & 7 & 8 \end{array} \right), $$ which I suppose is more easily described as "shift all entries to the right one, wrapping as text does". Then one also applies the symbol permutation.]

Applying this to the middle matrix in the bottom row gives the second matrix you've provided.

mollyerin
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  • You are right. It was more complex than I thought. Could you recall what was the first pattern you saw which gave you the idea? – nize Jan 25 '15 at 12:50
  • The thought process was: The transition between the end of a row and the beginning of the next is clearly a rotation. However, some checking convinced me of the fact that there's no permutation $p_1$ taking a left matrix to a middle matrix that works for both rows 1 and 2. Once you're convinced of that, it seemed like the only way to have a simple rule that would actually work was to include a permutation on the symbols. I think once you have the "permute the symbols" idea, the rest is easy (you just sort of try things on the first two matricies until something works). – mollyerin Jan 25 '15 at 12:56
  • I see. However, the rotation I guess was there only to confuse? It actually didn't provide any help for finding the transformation from left to right? – nize Jan 25 '15 at 13:55
  • Yeah, now that you mention it I guess it wasn't really any help... Maybe it was just nice to feel like the symbols hadn't been put on randomly. – mollyerin Jan 25 '15 at 14:18