The puzzle is as follows:

Figure 1.1 shows a kitchen floor that is made up of 30 squares whose sides measure 1 cm in length and in Figure 1.2 a tile that is made up of 5 squares whose sides also measure 1 cm. How many tiles congruent to figure 1.2, at most, can be placed on figure 1.1, without overlapping or leaving the exterior edges?

Sketch of the problem

The choices given are:

  1. 6
  2. 4
  3. 3
  4. 5

It seems that the intended meaning is that overlapping should be minimized, although this is not specifically stated. It appears there is no way to cover the figure without overlapping the small figure, if overlapping refers to not leaving the contour of the figure. Considering this, does a way to minimize overlapping exist?

This puzzle is somewhat of an adaptation from an APA exam of late 1970s and it appears to be based on Thurstone's and Catell IQ tests of such period.

I'm not sure what would be the right interpretation of "without overlapping or leaving the exterior edges". I think it means not trespassing those. However, no matter how many times I've attempted to rotate the second figure, I cannot seem use only the smaller figures to completely title the larger one. In other words, it is not possible to rebuild the first figure by only using the second figure.

If overlapping the small figure is allowed (I'm not sure) I get 7 pieces, which is off by one from the given choices.

What could be wrong here? Can someone help me?

  • $\begingroup$ I think your interpretation of the problem is slightly wrong. Instead of minimizing overlapping, the problem asks the maximum number of small figures which can be put on the larger one, no overlapping allowed. As written it is not asking you to cover all of the large figure, just the most you can without overlap. $\endgroup$
    – bobble
    Mar 11, 2021 at 15:18

1 Answer 1


As it appears that there is no way to do the figure without overlapping the small figure

There is a way, though (if you allow reflections):

enter image description here

  • $\begingroup$ That's quick!. I maybe dumb with these kind of questions which makes me sad but your answer is exactly checking with the right answer. I wonder why I didn't noticed. $\endgroup$ Mar 11, 2021 at 10:05
  • 1
    $\begingroup$ No problem, happens to all of us sometimes. $\endgroup$
    – Glorfindel
    Mar 11, 2021 at 10:14

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