The puzzle is as follows:

Figure 1.1 and Figure 1.2 shown are made up of congruent triangles. Assuming you must place tiles congruent to figure 1.2 to cover all the triangles in figure 1.1, without the tiles overlapping or going off the exterior edges. What is the maximum number of tiles that you will use?

Sketch of the problem

The choices given are:

  1. 4 tiles
  2. 6 tiles
  3. 5 tiles
  4. 7 tiles

Regarding the intepretation of the word overlapping. I believe upon referring back to the source it seems that the intended meaning is that it allows overlapping inside the figure but not tresspassing the exterior edges or the contour. This overlapping seems to be required to be the least as possible.

Regarding the source, this seems to be an adaptation from an old IQ test taken from an APA exam from mid 1980s and probably an adaptation from Leon Thurstone/Catell tests.

I've attempted to put in different ways the tiles over the picture which is presented but no matter how many times I turned the original figure upside down and so on, I am ending with more tiles than what it is offered in the choices.

Could it be that there is more than meets the eye here or what?. Can someone help me here?.

  • 5
    $\begingroup$ Figure 1.1 has 26 congruent triangles and 1.2 has 4 triangles. So There would not have an answer. $\endgroup$ – George Mar 11 at 6:41
  • $\begingroup$ @George This question has been updated to reflect changes. It appears to be that the overlapping of the figure it is allowed but the requirement that it might be intended is that to minimize the number of overlapping and without tresspassing the exterior edges or the contour. $\endgroup$ – Chris Steinbeck Bell Mar 11 at 10:12

As George points out, there are 26 triangles in 1.1 and 4 in 1.2, so 6 copies of 1.2 won't be enough (they can only cover 6*4=24 of the 26).

Here's an example of 7 copies covering all 26, with some overlap:


  • $\begingroup$ It's very reasonable what you mentioned and I went back to the original source and it seems that the intended meaning seems to be to reduce at maximum the number of overlapping of such figures and such overlap refers not overlapping the exterior edges or the contour of the figure for such reason I've updated the question. $\endgroup$ – Chris Steinbeck Bell Mar 11 at 10:21

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