How to Play Binary: seven rules that solve it
A binary puzzle has only three rules, and almost all of the solving comes from two of them. Every puzzle here is checked by an independent solver that uses only deductions a person can make, so nothing below is a shortcut around guessing — it is the whole method.
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A pair forces its opposites
Two identical symbols side by side must have the opposite on both ends, or you would get three in a row. This is the most productive rule in the game and the first thing to scan for.
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A sandwich forces the middle
When two identical symbols have exactly one empty cell between them, that cell must be the opposite. Looking for this shape is faster than checking every cell in turn.
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Count to the limit, then fill the rest
Each row and column holds equally many of each symbol. Once one symbol has reached its quota in a line, every remaining cell in that line is the other symbol. Finished lines are free cells people walk past.
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Two left in a line still constrain each other
When a line needs one of each and has two cells left, check whether either choice would create a triple or duplicate another line. Usually one of the two is already impossible.
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No two rows may be identical, and no two columns
A line that is one cell from matching a completed line must differ in that cell — so the cell is forced. This is the rule people forget, and it is the one that cracks the last quarter of a hard puzzle.
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Work the fullest lines first
A line that is nearly complete carries the most constraint. Sorting your attention by how full a line is turns a scattered search into a short one.
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Re-scan the crossing line after every fill
Every cell you place belongs to a row and a column. The new deduction is almost always in the perpendicular line, not somewhere else on the board.
These puzzles are verified solvable by ordinary deduction, so if you are stuck the next step is a rule you have not applied, not a cell you have to guess. The duplicate-line rule is the one most often left unused.