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A square one inch wide and one inch in length can be cut into 3 equal parts. Show that there is one of the three parts which contains 2 points at a distance of a least one.

I know the square has an area of one. So if you have 2 points by the pigeon the two point go in one square .

But if it is cut into three part each triangle will be 1/2 in length and wide 1/2 and have a distance of $\sqrt\frac{1}{4}$

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    $\begingroup$ Ask yourself: In which of the three parts are the corners of the square? $\endgroup$ – Steve Kass Feb 23 '14 at 19:37
  • $\begingroup$ but how can a square be three equal parts i can see 4 equal parts but not 3 $\endgroup$ – Fernando Martinez Feb 23 '14 at 20:19
  • $\begingroup$ Divide the square by vertical lines? That's one possibility for congruent pieces. There are plenty of options for pieces of equal area. $\endgroup$ – Mark Bennet Feb 23 '14 at 20:29
  • $\begingroup$ I see so width of my square is one but the lenght is one third $\endgroup$ – Fernando Martinez Feb 23 '14 at 20:52
  • $\begingroup$ imgur.com/j5V0mA5 $\endgroup$ – Steve Kass Feb 23 '14 at 20:55
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At least one of the pieces will contain at least 2 of the corners of the square.

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