Binary Balance

Controls

• Tap a cell to cycle blank, 0, 1. With the keyboard, move with the arrow keys and type 0 or 1; Backspace clears; Space cycles.
• Notes (or the N key) records which digits a blank cell could be, without filling it.
• Check lists any rule that is broken; Hint names the rule behind one cell it can deduce from the board as it is.

The rules

• Each row and each column contains equal numbers of 0s and 1s.
• No three equal digits sit next to each other horizontally or vertically.
• No two completed rows are the same, and no two completed columns are the same. A row may equal a column.
• Bordered cells are fixed clues and cannot be changed.

Scoring, saving and limits

Puzzles finished without a hint are ticked as solved on this device. The difficulty label is measured: intro and standard boards can be finished with triple prevention and balance alone; advanced boards need at least one deduction that considers every way to finish a line.

Your grid, notes and solved puzzles are kept on this device. Download a backup to move them; Clear this game deletes only Binary Balance's data.

Uniqueness was proved for every board by an exhaustive solution count that stops at two. Hints reason only from the board as it is; if your entries already break a rule, the hint points that out first.

Questions

Where should I start?

Look for two equal digits side by side, or with one gap between them: the cells next to (or between) them must be the other digit, or there would be three in a row. Then fill any line that already has half of one digit.

Can a row be the same as a column?

Yes. The rule only forbids two identical rows or two identical columns; a row and a column are compared separately.

Does every puzzle really have one answer?

Yes. Each board was checked by a solver that counts every solution and stops at two; only boards with exactly one were kept.