The rules of Binairo are simple:

1) Each row and column must have an equal number of black and white circles.
2) There can be no horizontal/vertical line of three like-color circles.

Starting from a position of fixed circles (indicated by those with dots in the center), one can complete a grid using logic.

In the puzzle below, provided by this website, I have made at least one mistake (hopefully no more than one), and I know this because filling in any of the empty cells would break one of the rules. I am not asking you to solve this puzzle for me necessarily, but rather, I want to know: Is it possible to determine logically where I went wrong without starting over from scratch or randomly erasing cells? What would you do to correct your mistake if you found yourself in this position while solving the puzzle? Example Puzzle

  • $\begingroup$ Not a definitive answer, but are you using the undo-redo arrow buttons above the puzzle grid? $\endgroup$ – Nautilus Feb 7 at 11:20
  • $\begingroup$ Those buttons provide little in terms of methodology. I was hoping for more of a deductive option. If the answer ends up being "no", then they will suffice for the future, if the situation occurs again. $\endgroup$ – Anonymo-5000 Feb 7 at 19:39
  • $\begingroup$ No, there's pretty much no way to do it without essentially re-solving the whole puzzle. Logical deductions can ripple through the grid, and if any number of them can be wrong the fastest option is just restarting. $\endgroup$ – Deusovi Feb 8 at 14:31
  • $\begingroup$ As Deusovi says, it is practically impossible to correct an error that isn't quickly noticed. In this particular grid, you have 11 cells in error. $\endgroup$ – Daniel Mathias Feb 9 at 4:36

I would be inclined to start over.

However, since that's the boring answer here is a thought of how to fix it.

  1. Put a black in the top left and a white in the bottom right since that satisfies both directions.
  2. Choose one of the configurations: B in the top right and W in the bottom left or other way around.
  3. Now note that all your rows are correct and exactly two columns are wrong by exactly two (or other way around)
  4. So go down the two wrong columns (or rows) and see if there is a situation where there is a white in one and a black in the other that are both unfrozen (no dot). Swapping them will either fix it or make it worse. So either fix and you're done or move on.
  5. If that doesn't work, go back to 2 and try the other way.

Beyond that, I can't think of any way to find the error that doesn't involve redoing the logic from scratch.


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