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Images are linked from the Swedish study site pluggakuten.se.: https://www.pluggakuten.se/trad/matrigma-10/

Anyone who can explain?

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I think the basic answer is that these are poorly designed puzzles. In an interview, they might be interesting because someone could talk through how they are thinking about them, but to present them like this is silly, imho.

Here's an approach that gets to an answer, but is still basically unsatisfactory.

Firstly, consider that the dots and extra lines primarily are there to provide a direction for the triangle. Of course, the first triangle then doesn't have a direction. But, actually, the remaining triangles then establish that the direction is simply determined as the opposite of the side that's parallel to one of the 4 cardinal directions.

So we rewrite the matrices as follows:

\begin{array}{ccc} \uparrow & \leftarrow & \rightarrow \\ \downarrow & \rightarrow & \uparrow \\ \leftarrow & \uparrow & ? \end{array}

and

\begin{array}{ccc} \leftarrow & \uparrow & \downarrow \\ \rightarrow & \rightarrow & \rightarrow \\ \downarrow & \leftarrow &? \end{array}

In the first question, each row and column has a pair of arrows pointing in opposite directions. So the remaining arrow has to point down. It's $(\rightarrow,\downarrow)\cap(\leftarrow,\downarrow)$.

But now there are two possible answers. I'd guess the 3rd answer simply because there are no cases in this question with 3 lines. You could argue for the 4th answer because no row or column has the same figure throughout. Maybe that's better. Okay 4. Whatever.

In the second question, each column has a pair pointing in opposite directions. So it's a member of $(\uparrow,\leftarrow)$. And then, ugh. We've got two lines with two different patterns. One all the same and one all different. So pick one of those? Or introduce a new one? Bottom row is $90^\circ$ rotation of the top? I don't know.

I'm going to pick that it's $\uparrow$. I'm claiming it's in $(\uparrow,\leftarrow)$ from the column "pattern", and not in $(\downarrow,\leftarrow)$ because rows are all the same or all different. Which is a serious stretch given that I only have two examples, one of each.

Anyway, that makes it number 3.

Okay, so I'll change my first answer to number 3, because there's a clear pattern that all questions of this sort have answer 3. Oh, wait. Maybe the answer moves down by one each time. So it is 4,3 after all.

As I said, it's a bit silly.

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