Making a bigger square

(Presented at a dinner table in Marktoberdorf summer school 2008)

You start with four point in a plane, making a square. You can move any point A by:

  • Choosing another point B in the plane;
  • Mirror point A with respect to point B, jumping A over B.

The question is: can you arrive to a configuration where you have a bigger square formed by the points? If not, why not? Note that the final square can be rotated with respect to the original square.

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One Comment on “Making a bigger square”

  1. simpple Says:

    The solution is very simple and logical… But it can take time to see it, which makes this a quite interesting puzzle (at least for me).


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