# Incorrect solution to IQ test question from Jordan Peterson video? Shorthand:

Horizontal rectangles called bars, vertical rectangles called poles. Horizontal groupings called rows, vertical groupings called columns.

Ba = Black, Bu = Blue, Y = yellow

Sequence is counted from top-right to bottom-left.

The following patterns are those that could be realized with any of the final shapes put into place:

1. In every column, exactly two poles of the same colour is present.
2. In every column, exactly two bars of the same colour is present.
3. Sequence of colour for bars goes Ba, Ba, Y, Y, Bu, Bu, Ba, ?, Bu
4. Sequence of colour for poles goes Y, Y, Bu, Bu, Ba, Ba, Y, ?, Ba
5. The triangles in every column, row and right-diagonals are all of distinct colours.
6. A yellow pole is always above black bar, a blue bar over a yellow one and a black one over a blue one.

$$P(x) =$$ number of patterns adhered to by the $$x$$th option.

$$P(1) = 1 + 1 + 0 + 1 + 0 + 0 = 3 \\ P(2) = 0 + 1 + 1 + 0 + 0 + 0 = 2 \\ P(3) = 0 + 0 + 0 + 0 + 1 + 1 = 2 \\ P(4) = 1 + 0 + 0 + 0 + 0 + 0 = 1 \\ P(5) = 1 + 0 + 0 + 0 + 1 + 0 = 2 \\ P(6) = 0 + 1 + 1 + 0 + 0 + 0 = 2 \\ P(7) = 1 + 1 + 0 + 1 + 1 + 0 = 4 \\ P(8) = 1 + 0 + 0 + 0 + 0 + 0 = 1$$

The seventh option is the correct one, from what I can tell. The third option didn't even score second. Is it me who is mistaken, the test, or Jordan Peterson (or whoever made his presentation)?

EDIT:

More patterns I've noticed; every triangle on the left-diagonals are of the same colour. Every pole on the left-diagonal are of different colours.

• Counting the number of patterns adhered to is not a good way to solve this kind of questions, because some patterns make more sense than the other, or more specific, or more generic, or more natural, etc. Also, there is a possibility there are patterns that you haven't considered yet. Apr 5 at 4:21
• @justhalf "Counting the number of patterns adhered to is not a good way to solve this kind of questions, (...)", as opposed to what? Determining which ones are, as you say, more sensible? I cannot fathom an objective way to determine what is more sensible, and even if one were to figure out what is more natural through some studies, why does the naturalness of a pattern mean that is should be weighted more highly? And how much more highly should it be weighted? So much arbitrarity. If this is inherent to IQ then it truly is subjective nonsense. Apr 5 at 4:26
• "If this is inherent to IQ then it truly is subjective nonsense" Indeed. Apr 5 at 4:36
• @justhalf I see. If it isn't too much trouble, could you perhaps point me to some resources where the methodology behind determining the sensibility and naturalness of patterns in IQ tests is discussed? I've started some research into it. Apr 5 at 4:39
• My 7YO niece once complained that her test result was marked wrong: She was given 2,4,8,... and had answered 13. .. The OEIS currently has 4,862 results for 2,4,8, and 126 results for 2,4,8,13. However, I doubt that she was using Mian-Chowla, (2^i)*(13^j), or any of the others, as she wasn't very good at adding two numbers. I suggested, kindly, that she give this one to the teacher. Jun 30 at 9:48

Without watching the source video, and ignoring the options given (so just looking at the grid of symbols as a self-contained PSE puzzle), I see:

Every symbol has an inverted triangle in one of three colours.
So far we have three yellow and three blue.
So I would expect the missing symbol to give us a third black triangle.

Every symbol has one of three combinations of rectangle (blue over yellow, yellow over black, black over blue).
So far we have three "yellow over black" and three "black over blue".
So I would expect the missing symbol to give us a third "blue over yellow" rectangles.

AND every symbol in the grid (so far) is unique.
Adding the missing black triangle with "blue over yellow" rectangles completes the set giving all nine possible combinations.

So I think the answer is pretty clear, but I can understand the unbalanced arrangement of the rectangles being a distraction. There is one of each triangle colour in every row/column, but the rectangles have repeats in some rows/columns but not all, which is ... unsatisfyingly messy.

• I got the same result - but, you know, these IQ tests often have multiple answers - and the idea is to find the one which is 'least complex'. That last sometimes has an underlying US/anglo-centric bias. Jun 30 at 9:40