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I found some sample Mensa IQ test questions at the Mensa Singapore website. There were 8 questions inside it. I managed to answer most of them without too much problem, however, I could not answer the last one. This is the question:

the test question

I could not figure out the pattern that governs which part in each square is shaded. The most that I could find out is that when the first four pictures are added(inclusive of overlapped parts), the last picture is produced, so the answer is D. However, I think that is wrong though, and even if it is really D, there is a way better explanation that explains why it is D. Any help in this puzzle is appreciated. Thank you.

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My intuition is that the answer is D, for the following reasons:

  • As we go from left to right, the number of highlight squares goes ?, 3, 2, 1. So we would expect the answer to have 4 highlighted squares, as in A and D.

  • As we go from left to right, the background color goes ?, white, black, white. So we would expected the answer to have a black background, as in B and D.

As a result, I think the answer is D.

This relies on seeing each picture as having a background color, with some number of squares in the foreground of the opposite color, with a extra highlight drawn around the foreground squares.

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My answer is D as well but I got to it slightly different way.

From right to left number of small, quarter, squares increases by 1 every step and colours get negated every step. So it looks like that (w for white and k for black background):

'squares':   (?) 4 - 3 - 2 - 1 - 0
'background':    K - W - K - W - K

So there are four squares on black background, therefore squares are white and it's option D.

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