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I'm trying to find a solution for the following puzzle. A friend sent it to me and I know that he didn't create it and that's about it for the original source; I tried to find it on the net but I couldn't make it.

Here it goes:

$$\begin{array}{|c|c|c|c|c|}\hline10&9&6&12&3\\\hline7&14&11&7&21\\\hline3&8&2&1&4\\\hline1&6&4&2&9\\\hline13&9&11&16&\color{red}?\\\hline\end{array}$$

I tried with sums, differences, products, ratio and a difference table but I couldn't find a solution.

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  • $\begingroup$ How do you know it's about patterns and calculations? Why not cipher for instance? $\endgroup$ – Arnaud Mortier Sep 15 at 6:56
  • $\begingroup$ I assumed it was because I exchange only puzzles of this kind with my friend. But you're right, I can't rule out your hypothesis. $\endgroup$ – D.K. Sep 15 at 7:01
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The answer is 11, I forgot to try linear combinations on the columns, I'm an idiot.

For example, the first element of the fifth row (a5,1 = 13) comes up as a result of the following operation:

a5,1 = (a1,1 + a2,1) - (a3,1 + a4,1)

So the answer is: (3+21) - (4+9) = 11

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