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This question made me wonder if an open problem had ever been solved via collaboration on StackExchange.

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    $\begingroup$ Yes. There are some papers (and at least one masters thesis) which started as MSE questions/answers. $\endgroup$ – Asaf Karagila Oct 10 '14 at 1:13
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    $\begingroup$ See the thread Papers that originated on math.SE $\endgroup$ – Antonio Vargas Oct 10 '14 at 2:13
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    $\begingroup$ Similar topic at MO: Best of MathOverflow $\endgroup$ – Martin Sleziak Oct 10 '14 at 5:39
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    $\begingroup$ Not solved, don't know if open problem. But many of us wonder. About this one. $\endgroup$ – leo Oct 15 '14 at 15:13
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    $\begingroup$ One user gave a seemingly new proof of the irrationality of root two; not an open problem of course, but original: math.stackexchange.com/questions/917983/…. $\endgroup$ – user117644 Oct 20 '14 at 10:00
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    $\begingroup$ @mistermarko That is not a new proof. $\endgroup$ – MJD Oct 20 '14 at 12:03
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    $\begingroup$ You really need to provide a link to an earlier instance of it then. He genuinely thought it was new and no one could correct him. $\endgroup$ – user117644 Oct 21 '14 at 5:40
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Ian Wanless gave an example of a pair of orthogonal complete Latin squares of order 12 here.

The existence question was posed as a problem by Keedwell in "Some problems concerning complete Latin squares" (1974).

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