# 90, 135, 180 degrees, but no 225, find the pattern

Source: A question from an online test the psychology department at my university asked test subjects for an experiment. They gave me permission to share the question online.

I originally asked my question Math Stack Exchange, but was told it was inappropriate there. So asking on Puzzling Stack Exchange instead.

Say we have the following pattern.

I want to know, given the possible 4 choices, which figure should come next.

1st choice:

2nd choice:

3rd choice:

4th choice:

My thought process in approaching this problem: The angles made by the intersection of arrows in the initial three squares are $$90$$, $$135$$, and $$180$$ degrees. However, there's no angles in the four choices for the next square in the pattern with $$225$$ degrees, so I'm confused. Which one of the following patterns is correct?

The most likely option is

2

because

the lower arrow rotates 45° clockwise with each step (E to SE to S), so it should point SW and only option 2 has such an arrow. (The upper arrow should, by the same logic, point south, but no option has that.)

The correct option is:

There is no correct option

Why?

Look at the first arrow. With each progression, we see that it rotates by 180 degrees, but there is no option with the first arrow pointing downwards. However if you look at the second arrow we see that it turn by 45 degrees clockwise.

So according to this the correct option most likely or closest to the correct answer is:

Option 2

I also picked #2 as best answer. I perceived the arrows as Force Vector arrows and I did simplistic vector analysis. In vector analysis the length of arrow is the magnitude and the arrow head is the direction. With two arrows you combine them. Or separate them, to facilitate depicting where the force is pushing, or pulling, the object (you). Slide both tails to you (the origin) but maintain orientation, in order to estimate the resultant sum of the two forces.

• I believe the other arrow was supposed to point down. Possible error on the question response, due to typo with the arrow’s direction. Commented Jan 18, 2023 at 10:19