Progressive matrix - crosshatched vertical and horizontal lines in squares

I came across this puzzle in the subreddit r/puzzles, gave it a try, and couldn't solve it. It seems like no one else could either.

Reverse image search found it on a site called IQ certificate, so I'm assuming that is the source.

I'm really curious, would appreciate if anyone can shed some light on it for me.

• These "IQ test" sites are mostly a ploy to get your phone number so they can charge you for some service that you do not want. or if you score low enough enlist you to help a "Nigerian prince" for a hansome if ficyicious reward. Don't expect quality Aug 9, 2020 at 9:13

I will go for the top-left because

Think of the game Set. https://en.wikipedia.org/wiki/Set_(card_game).

The horizontal lines in rows and the vertical lines in columns follow the rule "all counts equal or all counts different".

The top row has 2-2-2 horizontal lines, the middle row has 3-1-2, the bottom row has 1-1-? which must be 1-1-1. The missing square has 1 horizontal line.

The left column has 1-1-1 vertical lines, the middle column has 1-2-3, the right column has 3-2-?, which must be 3-2-1. The missing square has 1 vertical line.

The only choice with 1 horizontal and 1 vertical line is the top-left one.

PS: A maybe simpler but equivalent formulation can be given as:
The number of horizontal lines in rows and vertical lines in columns is always a multiple of 3.

Edit: Corrected my answer

(Bottom right option)

because

The logic of the horizontal lines:

if you think row-wise and look at the right most tile of the first two rows, the horizontal lines are equal to the number of horizontal lines left if you were to superimpose the left tile over middle tile and take away the lines that overlap. Applying this logic to the third row gives the bottom right tile 0 horizontal lines.

The logic of the vertical lines:

Look at the first two rows again it is very similar to the logic of the horizontal lines. But instead in the right most tile, the number of vertical lines is the remaining vertical lines left after the superimposing of the left and middle tile and then taking away of vertical lines with the addition of an extra vertical line. This gives the bottom right tile 3 vertical lines when we apply the logic to the third row.

• Following your logic of taking the first and second draw on each raw and cancel out any horizontal lines that overlap, would not give you the third draw in the second raw.. As well as if you take the bottom raw and following this logic you'll actually get all the bottom answers and not bottom middle and top middle like you said.. Good try though Aug 8, 2020 at 23:44
• Check it now this is definitely correct
– PDT
Dec 25, 2023 at 9:54

The middle column of squares has on each square 4,4,4 rectangles and 2,2,4 squares respectively.

The right column of squares has 4,4 rectangles and 8,5 squares respectively. If we add to that column the top right coloured square then we have for the three squares of that column

4,4,4 rectangles on each square and 8,5,5 little squares for each.

Here is another interpretation:

First we replace the question mark with the first coloured quadrilateral from the third column. Then we count the straight lines contained in each quadrilateral to obtain the results shown in the drawing below.

• Who defines what's a square? According to you, you only count it as a square when there is no additional lines crossing it.. However if that is the case the first column doesn't follow your pattern and in general it seems like it's a very unlikely as it ignores other factors like position and even there is not seems to be a clear pattern in the rectangle's numbers.. Nice try though, I personally have also explored this route of counting squares and etd c quite alot Aug 8, 2020 at 23:50
• To me your drawings are made from rectangles and squares. I based my answer on this fact. Additionally, I based my conclusion on the second and third columns. Counting the lines inside the three squares yields inconclusive results. I hope this is helpful. Aug 9, 2020 at 1:54