Does anyone know the answer and the logical explanation? It is driving me crazy.
I don't quite like "uniqueness proofs" for next term questions, so here is hopefully a more direct approach.
There are two types of dots; I have colored them for your convenience.
The red dots are paired up, and go down one row every turn, alternating between the first/second and fourth/fifth columns.
The purple dots inhabit a smaller 3x3 grid taking every other row and column. Every term these dots move up by one square, wrapping around and moving left when reaching the top.
At any rate:
This comes to the same conclusion as Rand does and suggests that the correct answer is the bottom left answer.
In each 5x5 square, one row contains two green dots, two rows contain one* green dot each, and two rows contain **no green dots.
The row with two green dots is, respectively through the sequence, the 1st, 2nd, 3rd, and 4th row. In the final square, it should be the 5th row.
The two green dots in that row are, respectively through the sequence, to the left, right, left, right. In the final square, they should be to the left.
Now the only possibility among the six options for the final square is
the bottom left one.