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I remember being presented a mathematical puzzle some years back that I still can't solve. The problem is defined as follows:

We have two points on a plane, and using only a compass, how do we find other two points, so that all four of them would be vertices of a square?

I'm not sure whether the first two points were supposed to be vertices of the same edge of a square or not, so solutions to both variants are welcome.

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    http://en.wikipedia.org/wiki/Mohr%E2%80%93Mascheroni_theorem and http://www.cut-the-knot.org/do_you_know/compass.shtml2012-03-05
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    The trick is to figure out how to construct a pair of points which $\sqrt{2}$ apart...2012-03-05

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