Is there any logic for finding the next shape in the blank?
I think it's an hard one.
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As the comments pointed out, these types of problems can be really ambiguous. Here's my guess. Note that out of the four options, the main thing that is different is the number of white shapes. So we need to come up with a rule that tells us how many white shapes should be in the last column.
Scanning along the first row, there seems to be the following rule:
Scanning along the second row, there seems to be the following rule:
Scanning along the last row, we see that the triangle on the left is in the same position in both columns, implying that only one of them will be in the last column. Furthermore, we see that the triangle on the right is in a different position in both columns, implying that both of them will be in the last column.
Thus, my guess is that the answer is the leftmost option labelled $(4)$, since it has $1+2=3$ white triangles.