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Jan 11, 2016 at 17:51 comment added Włodzimierz Holsztyński It turns out that Wlodek Kuperberg has posted a similar counter-example to my conjecture on FB about 3h before the katz's solution on MO. He had a unit disk inside a $5x2$ rectangle. Each example has its own subtle advantages (while my conjecture was rather easy--after the fact).
Jan 11, 2016 at 17:27 vote accept Włodzimierz Holsztyński
Jan 11, 2016 at 15:29 history edited Mikhail Katz CC BY-SA 3.0
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Jan 11, 2016 at 15:08 history answered Mikhail Katz CC BY-SA 3.0