4
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enter image description here

What shape should go in the empty square?

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6
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The answer is:

upper right triangle

Because:

To get the third square, flip the first square vertically and XOR it with the second square on the row below (wrapping around back to the top row if necessary).

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1
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My guess:

Nothing goes in the empty square.

Explanation:

For each row, the third square is the path difference between a modified second and first square. You modify the first square by flipping it across the X-axis. You modify the second square by reflecting across the main diagonal and finding the union of the two shapes.

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0
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Square

Reasoning

The final column is always a combination of the previous two, in multiples, Inverse.. Not as obvious in the second row as both shapes are rotation (<90deg in segments of 90deg) agnostic, however with the square.. It's result is always a square..

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0
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Nothing

My Reasoning:

Working horizontally through each row it is the 2nd shape shrunk horizontally by 50% and then mirrored across a vertical line in the middle of the square. The first shape is then cut out of the result of the shrinking and mirroring. A Square shrunk by 50% and then mirrored would be the same size as the original squareso the image from position 1 would fit directly over it leaving a blank image.

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0
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It could be:

a circle

Explanation:

Counting the times that the triangle pokes the roof, from left to right, we get this sequence:
010 / 100 / 101

And using this to determine what goes where:
1 - Ball,
10 - Square,
0 - Nothing

It creates a pattern that could be interpreted like this:
Row 2: Combines them like this
01+0 / 10+0 / 10+1
Ball & nothing, Square & nothing, Square & ball.

Row 3: Only counts the last number
01+0 / 10+0 / 10+1
Nothing. Nothing. ball

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