I took an IQ test at Psychology Today(https://www.psychologytoday.com/intl/tests/iq/culture-fair-iq-test) and encountered this question which I wasn't able to solve:
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$\begingroup$ Welcome to PSE (Puzzling Stack Exchange)! $\endgroup$– Will.Octagon.GibsonCommented Jun 13 at 17:34
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4$\begingroup$ Goodness, I'd need a week for the test judging by this question... $\endgroup$– Peter - Reinstate MonicaCommented Jun 13 at 23:43
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7$\begingroup$ I always find those questions terrible. There's often a likely explanation resulting in a "wrong" answer -- by which we don't really mean wrong, of course, just that the designer didn't think about it :'( $\endgroup$– Matthieu M.Commented Jun 14 at 14:24
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2 Answers
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It is the first option (from the left).
If you look at the rows, all the squares are rotating one step clockwise around the line per tile…
Here is a diagram to show what I am on about:
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I have the same answer as PDT, but reached it by entirely different reasoning.
Group them by column, not row. In each group, rotate the middle figure by 180 degrees, and overlay it onto the top one. This produces the bottom figure.
Diagram:
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7$\begingroup$ The two solutions can't be the same thing in disguise due to the different ways of grouping. I think it's just coincidence they both work. It makes me wonder what kind of quality control went into making this puzzle. Did they carefully choose the answer options such that only one matches a simple solution? Did they know there were these two solutions? I would find it interesting (and cause for embarrassment for Psychology Today) if someone were to find a satisfying solution pointing to one of the other provided options. $\endgroup$ Commented Jun 14 at 0:51
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1$\begingroup$ @Peter-ReinstateMonica It's coincidence that the (i.e.) left column matches up, but no further coincidence that the other ones do, as the operation from PDTs answer is preserved under both "overlaying" and rotation by 180°. As there are a lot of similar possible "coincidences" (rotate the other one, XOR instead of overlay, ...) I doubt that it's intentional. $\endgroup$– ManfPCommented Jun 14 at 0:53
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1$\begingroup$ @Lichtbringer You may be rotating about a different axis than I mean. The axis of rotation is orthogonal to the plane the figures are in, meaning they stay inside of that plane as they rotate. If you instead use the line the rectangles are attached to as the axis of rotation (meaning the figure extends into the third dimension as they rotate), you would get the rightmost answer. But I would call that a reflection, not a rotation. $\endgroup$ Commented Jun 16 at 1:27