I've seen a lot of these types of puzzles in IQ tests, quizzes of various sorts, and I have never been able to figure out how to solve them. These generally involve two or more sets of geometrical figures with numbers written in them. These bear a certain relationship that we are required to find out.

For instance,

enter image description here

Now, in this particular problem I have tried everything I can think of: sums, products, squares. The sheer enormity of possibilities seems daunting to me, particularly when there is no apparent way to narrow things down.

I would like to know if there are some general tips to approach some problems, perhaps using this one (or any other suitable one) as an example.

  • 1
    $\begingroup$ The example you posted seems way underspecified. The second triangle doesn't even have a number in it? Where did you find this puzzle? $\endgroup$
    – xnor
    May 4, 2015 at 6:56
  • $\begingroup$ @xnor: Sorry, somehow forgot to add the number. Edited. Sorry. $\endgroup$
    – Gerard
    May 4, 2015 at 8:14
  • 1
    $\begingroup$ I still feel like there's going to be a lot of possible solutions. The center could just be 6 times the number on the right, for example, giving 12. Or, 3 times the product of the two smaller numbers, giving 18. So my first bit of advice is to check that what you're solving is likely to be a decent puzzle. Where are you encountering these? $\endgroup$
    – xnor
    May 4, 2015 at 8:26
  • $\begingroup$ @xnor: I found this one on an iq test. The answer for this is 24. Also, usually these puzzles require the use of all given numbers. However, it's all right if you find this one vague. You can use any other example you wish. My real question is about the approach behind solving such problems. $\endgroup$
    – Gerard
    May 4, 2015 at 8:48
  • $\begingroup$ Is the test multiple choice? Because it's possible that they restrict reasonable answers based on the options. $\endgroup$
    – Glen O
    May 4, 2015 at 11:06

1 Answer 1


When you don't have an idea, you have to try anything and see if it works! In IQ tests there are often far-fetched patterns, your job is to identify them following these general tips:

  • If different geometric shapes are involved, the "trick" is usually in their position, orientation and number of edges.
  • If colors are involved, identify the elements with the same one and count them (eg how many yellow items? how many red?)
  • If numbers are involved, the puzzle is almost always based on sums, subtractions, products, sometimes squares and factorials. Almost never divisions and roots.

In this particular case, we see that the triangle is an invariant, so improbably we'll find hints in it. The problem also involves small numbers and there are only 2 clues (the numbers in the first two triangles), significantly increasing the difficulty of the problem.
I think that in this case the answer is



The central number is the product of the three numbers in the vertices minus 6.


  • $\begingroup$ Are there any resources for more puzzles of this sort? $\endgroup$
    – Gerard
    May 4, 2015 at 12:31
  • $\begingroup$ @Gerard Google "IQ test online" or "IQ tests solutions explained" $\endgroup$
    – leoll2
    May 4, 2015 at 12:49

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