# IQ question involving patterns of lines joined together

This is an IQ question posted on Reddit. I believe the answer is D, but everyone is arguing that the correct one is A. I think it is D, because we also have to reduce the line which is not included in the top pattern of the right column, so as to have 8 lines as a total in the final pattern, as option D illustrates... if we put A, we will have 9 lines, but don't we also have to signify the reduction in the last pattern?

• It looks like red replaces the reduced line so A actually has 8 black lines plus the red bit as you want, whereas D has 7 black lines plus the red bit. Jul 12, 2023 at 12:57
• If u see the first column, it has a total of 9 lines at its bottom pattern, which occur from the sum of the 5 lines of the top pattern and the 4 lines of the middle pattern. In the second column, the bottom pattern has 8 lines , the blue circle and the replacement of the line with a fully blue circle, which occur from the sum of the 5 lines of the top patttern, and of the 4 lines, although the 4th line is replaced as we see with the fully blue circle and the blue circle with the white interior is also appeared onto one of the lines.... Jul 12, 2023 at 13:01
• so in the last one, we should have 4 lines, plus 3 lines which appear with one being a smaller one since in the mid pattern of the column it is a bit cut on the right, plus the small red line. so we hae a total of 8 items/lines Jul 12, 2023 at 13:01
• hexomino it reduces the line on the mid pattern, but shouldn't we also reduce the missing line on the top pattern? we have already included the red line, so if we choose 8 , won't we include the red line twice?? Jul 12, 2023 at 13:05
• this is actually kind of interesting: most people seem to read it left-to-right whereas you're reading it top-to-bottom. I do think that reading it left-to-right is a bit more compelling, as you can see that the two different circles perform consistent actions across the first two sets, whereas your argument relies on counting lines, which doesn't feel like it's as strong an argument to me. don't get discouraged, though - often these types of problems aren't as ambiguous as one would hope, and it's certainly not a bad thing to be able to think about things differently from everyone else Jul 12, 2023 at 13:17

As with most IQ pattern tests, it is possible to interpret it in multiple different ways, and reach multiple different conclusions. The intended solution is often the one that is the most "intuitive" (whatever that means - usually the most cohesive reasoning, with the fewest edge cases).

If the intended answer is answer $$A$$ (as I would argue), the image is read left-to-right, with each row forming a unit. The rules would be:

1. The hollow circle removes any parts of the lines inside it.
2. The filled circle removes the line it touches, but retains the parts inside it - coloring them red.

These rules are simple, follow similar logic to eachother, and can be verified using only the question part of the pattern (i.e. each rule appears in full twice). They also leave us with only one unambiguously correct answer: answer $$A$$.

If the indended answer is answer $$D$$ (as you argue), the image is read top-to-bottom, with each column forming a unit. The rules would be (as I understand your argument):

1. The line count of the two previous images are added to give the final line count
2. The filled circle, if present, replaces one of the lines
3. Non-line elements (e.g. red lines and blue circles) do not appear twice in the final image, but should be present if present in the two previous images

(and possibly more)

This reasoning does leave some questions unanswered, though, e.g.:

• Why isn't answer $$B$$ an option, having 7 lines and the red line present just like answer $$D$$ does?
(if your answer is "because one line should be shortened as it is in the previous image", then that raises further questions, e.g. why is the length of the line relevant when it hasn't been for the previous columns?)
• Why are lines and non-line elements treated differently, if they both depend on being present in the previous images (line count is added together, non-line count is not)?

As such, although it is certainly possible to come up with rules until answer $$D$$ is the only correct answer, this solutions appears less "intuitive" than the one we used for answer $$A$$.

• I would add that if the first reasoning is the intended answer one could come up with the picture of A even if no answer options are given. I don't think one could construct image D just from the rules in the second reasoning and the pictures in the question. Jul 13, 2023 at 7:14