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Exactly 3 of 7 circles here should be painted black to make the Masyu uniquely solved. Find them!


1 Answer 1


I've found one solution, through some logical reasoning followed by trial and error.

Ignore the bottom left figure
I first figured that the circle in position [2, 1] (Red) must be white, because if it were black, circle in position [1, 3] (Green) would not be able to connect. Then for similar reasons, the yellow and cyan ones can not both be black. The same is true for cyan and purple. A few more similar deductions, like blue, purple, and black can not all be black, left me with eight possible arrangements, so I just tried to solve them all. Only one of them has a solution, and the process of solving it showed that it is unique (I don't know how to prove that though)

Thanks to Skynet_0 for pointing out that one of my solutions is invalid.

  • 11
    $\begingroup$ Your left solution seems to have an error in the leftmost black circle and the rightmost white. $\endgroup$
    – Skynet_0
    Commented Dec 10, 2019 at 4:02
  • 2
    $\begingroup$ @Skynet_0 Thanks, I don't know how I missed that... $\endgroup$ Commented Dec 10, 2019 at 19:42
  • $\begingroup$ Very well done! :D $\endgroup$
    – athin
    Commented Dec 10, 2019 at 23:41

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