I have this mind puzzle which has bothered me the latest days.
QUESTION:
CHOOSE ANSWER:
.
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? :)
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.