# Figure matrix IQ Problem

Found an old IQ problem that came up in an earlier job search. Still don't know how to solve it. I tried counting the number of edges/ faces and flipping the diagrams, but I can't see the trick.

I'm going to propose the answer as:

D

First, take notice of:

The rotation of each piece, within each row. The first row is rotating the pieces counter clockwise. The second, clockwise; finally the third is counter clockwise again.

Secondly, take notice of:

The color scheme in each piece, within each row. The first row follows a pattern of white -> black. The second's pattern is black -> white, and the third's is white -> black.

Additionally, it can be seen that:

Within each row, a piece may alternate color, but outside of that, it's not repeated again. For example, the triangle in the first row is white then black, then not there. Same with the arrow in the third row.

This leads me to believe that all of the aforementioned points would remain true in the blank square, and as such our only logical options are:

A and D

Also, notice that:

Each row has two repeated pieces each. The first row is the triangle and the trapezoid. The second is the arrow and the proposal of the door-ish looking shape. Finally, the third is the triangle and the arrow.

With this, we can conclude that:

The answer is most likely to be D, since the arrow has already occurred twice in the row.

Note: I tried making sense with sides and lines, couldn't see anything significant there.

• Pretty sure you mean D not C? White should be top right black bottom right, and C has a repeated part Sep 21 at 1:36
• @BeastlyGerbil ah, correct lol 😂 I need sleep 😴 Sep 21 at 1:41
• No worries, pretty sure this is correct (now) :P Sep 21 at 1:41
• @BeastlyGerbil thanks! 😊 also made me notice one more thing by making me come back lol so I added that too. Sep 21 at 1:44

A short formulation, in line with ​the accepted answer

The white symbol reappears as black, mirrored horizontally, in the opposite corner. The black symbol is replaced with a new white symbol. Only D honors that.

• This is very clean, concise, and probably what the original intent was (or close to it). Well done! (+1) Sep 21 at 13:49
• This occurs from left to right across rows, and "new" means "hasn't been seen in this row to the left". Sep 22 at 0:20

For all of these questions, the real key is to look at the possible answers.

Many times, the testers have one real solution in mind with 3 fake solutions that are adjacent by one thing to the real one.

So, looking for majorities gives the following results:

3 times the right column is occupied, only 1 time the left => right column is correct

3 times the moon is present, only 1 time not => moon has to be present

3 times the door is black, only 1 time white => door has to be black

That is enough to choose D, but if you look further you will see even more things that D has in common with the majority of answers.

• I wonder if that holds true on the Mensa test? 🤔 Sep 21 at 13:29
• @Tacoタコス generally speaking yea, but the one I took had 8 possibilities = waste of time. And some IQ tests has no abcd, just empty box for drawing. Sep 21 at 15:08
• I would use this method to verify whether D would match and reason backwards from there because it is much faster, should only take a few seconds. If it isn't a match, you can always start over :). Sep 22 at 14:35
• @Mixxiphoid Thats a good idea too :) Sep 23 at 5:39

Two rules:

• Just disregard all symbols and rotate the rectangle as indicated such that the color matches to obtain D or A
• Finally to differentiate between A and D apply the obs. of @Redutin that the white symbol in each row must reappear in the next cell as flipped horizontally and black

I see no immediate logic in the symbols other than the color.