The arrangement in the square grid shown below has four-fold rotational symmetry and none of its squares (apart from the central one) has more than two neighbors. Of course there are very many such arrangements. This one, however, has a very special property, unique within all such(*) arrangements of 289 squares. (*) edge-to-edge connected, four fold symmetry, and fewest possible number of neighbors. Which?
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Best regards, jj Hints below, after some several blank lines. Hints: A) 289 = 15^2 + 8^2 B) Consider two copies of the arrangement C) Consider 289 copies of the arrangement P.S.: almost-spoiler at http://jjj.de/visual-riddle/visual-riddle.png