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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

Samthere
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java guy
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3 Answers3

45

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

Community
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kavi temre
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  • Beat me to it..! – Mark N Jun 29 '15 at 15:36
  • Man, I turned on gridlines in Paint and everything! – Bailey M Jun 29 '15 at 15:37
  • Same here: got the 1 new answer just as I finished drawing it. :( – Spencerkatty Jun 29 '15 at 15:38
  • ohhh !! finally i beat someone . This time i didn't care about the look and cleanness – kavi temre Jun 29 '15 at 15:38
  • MarkN , Bailey and Spencerkatty first time i beat someone – kavi temre Jun 29 '15 at 15:40
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    Correct answer. This question was asked in a interview – java guy Jun 29 '15 at 15:43
  • dont forget to mark it as a correct answer. – kavi temre Jun 29 '15 at 15:46
  • I'm sorry but this cannot be correct. You need to draw these lines exactly in the middle of the squares, and you would need additional lines to find the middle. This may be the "intended" answer, but you cannot claim that you have drawn squares of the same size unless you have a way to put the four needed lines in the right place. I think that's a fault of the question, not the answer. – Floris Jun 30 '15 at 16:49
  • @Floris Seriously??? Though if you are going to be that picky, why would you have to draw extra lines to find the middle? Why couldn't you rig up a contraption to help find the exact middle without drawing any extra lines? And even then wouldn't you always run the risk of being at the very least several femtometers off? – Warlord 099 Jun 30 '15 at 17:51
  • @Warlord099 - normally when you do a geometric construction there is the assumption that when you draw a straight line from point A to point B, it is a straight line from point A to point B. And the question states "draw straight lines", not "use contraption XYZ". So I consider that you have to solve the problem (of finding the middle of the squares, and drawing properly horizontal and vertical lines through those middles) using just straight lines. But then you need more than four. And indeed the assumption that the drawing has squares is implicit as well. – Floris Jun 30 '15 at 17:56
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    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. – Warlord 099 Jun 30 '15 at 18:10
  • The question is tagged with "geometry". Maybe I am just a stickler and this is the wrong place for me. – Floris Jun 30 '15 at 18:59
  • This was a interview question as mentioned earlier, so the interview just want to test your logical thinking. It is just a solution to the problem. Somebody can edit the question and answer for better clarity. – kavi temre Jul 01 '15 at 01:42
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Kavi Temre got this first, but here's my unnecessarily clear image:

Samthere
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6

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

Floris
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