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I've been struggling with this puzzle for the last few days.

We have square

$$\begin{bmatrix} 3 & 6 & 2 & 8 \\ 2 & 1 & 1 & 3 \\ 1 & 3 & 1 & 4 \\ 5 & 5 & 3 & ? \end{bmatrix}$$

Question is what number we should insert instead of question mark ?

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    $\begingroup$ The pattern that I see here, is that $(3+6)+1 = (2+8), (2+1) + 1 = (1 + 3)$, and $(1 + 3) + 1 = (1 + 4)$, and since $(5+5)+1 = (3 + 8)$, we could be right to conclude that $? = 8$. $\endgroup$ – астон вілла олоф мэллбэрг Oct 20 '17 at 9:52
  • $\begingroup$ 9. It's just a square of numbers. $\endgroup$ – Asaf Karagila Oct 20 '17 at 9:54
  • $\begingroup$ The answer is $42$. I'm sure you will be able to find an argument for that (e.g. a polynomial of sufficient degree and some evaluations of it), as you would for almost all other solutions... Now the real question is: How do we know which system was in the mind of the one forming the puzzle, do we know his level of mathematical knowledge and thus the depth of the solution he had in mind? :) $\endgroup$ – Dirk Oct 20 '17 at 10:01
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Each row or column $[a\:b\:c\:d]$ has the structure of $a+b-c+1=d$, so $? = 8$.

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