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This question already has an answer here:

Four coins lie on a table and form a square. Now you are allowed to jump with a coin over another one, in any direction, i.e. also diagonally or however. You always have to jump all the way to the other side, so that the distance between 'jumper coin' and 'jumped over coin' is the same before and after the jump.

Is it possible to form a larger square? If yes, how? If no, why not?

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marked as duplicate by Mike Earnest, JMP, Glorfindel, Rubio May 27 '17 at 9:56

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    $\begingroup$ Please include attribution, if you have got your puzzle from another source. $\endgroup$ – boboquack May 25 '17 at 9:30
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Lemma:

If we can get to position B from A, then reversing moves yields position A from B.

Proof

Since the reverse of every move is playable, our lemma is trivial

Using this lemma, we see that it is

Impossible

as

Starting from a larger square, if we let the four corners be (0,0),(0,1),(1,1) and (1,0) then all coins always lie on lattice points and thus it is impossible to get a smaller square. Since we can't get a smaller square from a larger square, we can't get a larger square from a smaller square by our lemma.

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  • $\begingroup$ You didn't prove your lemma :P $\endgroup$ – boboquack May 25 '17 at 9:38
  • $\begingroup$ @boboquack Fixed (◔_◔) $\endgroup$ – Wen1now May 25 '17 at 9:41

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