Source: Intelligence and How to Get It: Why Schools and Cultures Count (2009). pp. 7-8.

enter image description here

  The example that the problem-solver must follow is set up by the two figures in the top row of the left panel. The figure at the left in the bottom row then specifies what has to be transformed in order to solve the problem. The six figures on the right correspond to the answer alternatives. The solution of the problem requires you to notice that the figure in the upper left of the left panel is a diamond and the figure in the upper right is a square. This tells you that the answer has to be a square. Then you must notice that the bottom half of the upper diamond is divided into two, with the left portion in black. The fact that the left half of the figure on the right is also black tells you that the corresponding portion of the square on the bottom right must match the corresponding portion in the lower left diamond-that is, the entire bottom half must be black. Then you notice that to make the top right figure, one of the bars has been removed from the top left diamond while symmetry of the bars has been preserved. This establishes that you must remove one of the bars of the square at the bottom while preserving symmetry. Now you know that the correct answer must be the square at the bottom right of the answer panel.

My attempt

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Between #1 and 2, 2 orange lines remain, the blue is removed, and nothing is added. So in #3, the 2 orange lines remain. #3 has no blue middle line that can be removed. So how can the right answer be #5, where the green line has been added to #3?

  • $\begingroup$ You got the numbering wrong. As the text says, it goes on the top line first (1 left, 2 right), then bottom row (3 left, 4 right). Solving the puzzle is « If 1 gives 2, then 3 gives what? » and not the order you used (btw your reasoning is perfectly correct, you just did not follow the rule of the test) $\endgroup$
    – marsei
    Commented Apr 28, 2018 at 0:47
  • $\begingroup$ @marsei I don't understand your comment. What's the referent of 'it' in your 'it goes on the top line first'? $\endgroup$
    – user6479
    Commented Apr 29, 2018 at 16:45

2 Answers 2


It is a very simple question.

In 1, three vertical lines were occupying the top space in the diamond. In the lower half of the diamond, half the space was shaded and the other half was unshaded.

In 2, two vertical lines were occupying the top space in the diamond. In the lower half of the diamond, all of the space was shaded.

There was hence a net loss of one vertical line and increase of one shaded space. That is the same operation you should have conducted in 4.

In 3, two vertical lines were occupying the upper-half space in the square. Similarly, half the bottom-half space of the square was shaded. Therefore, there must now be in the empty space a square containing one vertical line and a fully shaded bottom-half space.

It was not the relative positions of the vertical lines that you should have considered, but the quantity thereof.

I hope I don't have to explain to you why there should be a square in the empty space.

Anyways, that was my interpretation of the question. Hope this helped.


As the text you provide explains, there is a flow of thinking involved:

  1. diamond-diamond / square - ? (answer: square - you got that one right)
  2. bottom half becomes filled (you got that one too)
  3. one stripe removed above

All this added yields the picture at the bottom right. You didn't notice, interpret or actioned on the stripe removal, perhaps.

  • $\begingroup$ Sorry, but how didn't I notice 3? In my post, I wrote 'the blue is removed'. $\endgroup$
    – user6479
    Commented Apr 27, 2018 at 2:54
  • $\begingroup$ @Canada-Area51Proposal well you might have noticed but interpreted it incorrectly $\endgroup$
    – AliceD
    Commented Apr 27, 2018 at 5:20
  • $\begingroup$ How can I remove a (middle) stripe in 3, when there's none? $\endgroup$
    – user6479
    Commented Apr 29, 2018 at 16:46
  • $\begingroup$ @Canada-Area51Proposal you can't. You can remove a stripe $\endgroup$
    – AliceD
    Commented Apr 29, 2018 at 17:07
  • 1
    $\begingroup$ @Canada-Area51Proposal This really gets into what a perfectly fair test question ought to be. Because in this case, two things were changed with respect to the stripes: 1) a stripe was removed and 2) a stripe was moved. Whereas in the other features (location of shading and shape), only one aspect was changed. Is that a fair question? That depends on what you believe about the test. $\endgroup$
    – Chelonian
    Commented Apr 29, 2018 at 17:22

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