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You can draw up to 4 straight lines in order to create 10 equal squares in the following figure:

puzzle of two squares

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45
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Please ignore my painting skill. i am not good at it

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  • $\begingroup$ Beat me to it..! $\endgroup$
    – Mark N
    Jun 29 '15 at 15:36
  • $\begingroup$ Man, I turned on gridlines in Paint and everything! $\endgroup$
    – Bailey M
    Jun 29 '15 at 15:37
  • $\begingroup$ Same here: got the 1 new answer just as I finished drawing it. :( $\endgroup$ Jun 29 '15 at 15:38
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    $\begingroup$ Correct answer. This question was asked in a interview $\endgroup$
    – java guy
    Jun 29 '15 at 15:43
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    $\begingroup$ First of all, the "question" most definitely is not a question. The title is a command and the body is a statement, so yes it is a poorly worded question. Secondly, I do not see "geometric construction" so that appears to be an assumption on your part. Thirdly, I assumed the question was about where to place the lines and not how to place the lines (seeing as the OP accepted this answer I am assuming I am correct). Fourthly, this answer most definitely should have a paragraph describing the placement of the lines to make up for its crude drawing. $\endgroup$ Jun 30 '15 at 18:10
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Kavi Temre got this first, but here's my unnecessarily clear image:

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  • $\begingroup$ Good one. We have same logical thinking $\endgroup$
    – kavi temre
    Jun 29 '15 at 15:44
  • $\begingroup$ Wait don't lines extend infinitely though? /s $\endgroup$ Jun 29 '15 at 16:18
  • $\begingroup$ Yeah, these are just segments. $\endgroup$
    – user5521
    Jun 29 '15 at 22:18
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    $\begingroup$ Well, if we're talking like that then that can't be the definition of a line in this context. The question said "you can draw up to 4 straight lines". If, however, a line was infinite, I wouldn't be able to draw it. ;D $\endgroup$
    – Samthere
    Jun 30 '15 at 10:27
  • $\begingroup$ @Samthere: Sure you can, the question says so :-) $\endgroup$ Jul 1 '15 at 12:42
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I need 12 lines - 8 to find the centers of the large squares (thanks Aragaer for noticing that we get the center "for free"), then 4 to create the 10 equal squares. You could argue that the 10 dashed lines are not drawn as part of the "creating squares". In fact, you could use a ruler to draw just the little orange "helper marks" in order to do the construction.

It does assume that the two initial shapes are squares.

enter image description here

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  • $\begingroup$ You could use just 8 dashed lines. Either 4 and 5 or 6 and 7 could be dropped, the other two will work. You do have the center of the image. $\endgroup$
    – aragaer
    Jun 30 '15 at 23:06
  • $\begingroup$ @aragaer Good call - I missed the center point. I will update. $\endgroup$
    – Floris
    Jul 1 '15 at 0:13
  • $\begingroup$ Well done Floris +1 for dotted lines $\endgroup$
    – kavi temre
    Jul 1 '15 at 1:44

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