What are the rules of Binairo?

Each completed row and column contains equal numbers of 0 and 1. Three adjacent equal values are forbidden horizontally and vertically. No two completed rows may be identical, and no two completed columns may be identical. Blank cells prevent completion.

Are the puzzles uniquely solvable?

Every offered board is generated by the pinned version 1 algorithm and checked by a bounded exhaustive solver that counts up to two solutions. A board is published only when exactly one solution is proved. Failed, ambiguous or exhausted generation produces an error and retry option, not a playable board.

How do cell marks and pencil notes work?

Choose 0, 1 or Blank and activate a non-clue cell. The fixed clues have an underline. Enable Pencil notes to toggle tentative 0 or 1 notes in a blank cell; both can be shown. Notes do not fill the cell or count as scored changes. Arrow keys, Home and End navigate; 0, 1 and Backspace mark the focused cell.

What does Check current marks reveal?

It explains conflicts derived from your current marks: too many of one value, adjacent triples, and duplicate completed rows or columns. It does not compare every unfinished cell with the hidden answer. Requesting a check makes an unfinished challenge practice only.

How are challenge scores measured?

A challenge is one fresh 6×6 puzzle with no timer. Each successful explicit cell-state change counts, including corrections and blanking; lower is better. Clue clicks, unchanged marks, selections and pencil-only changes do not count. Checks, answers, undo, restored progress and previously opened equivalent puzzles disable scored sharing. Scores are self-reported.

Can I undo, redo or resume a puzzle?

Undo and redo restore recorded marks and notes. The browser can save your settings and puzzle progress locally. Resuming regenerates the seeded puzzle and validates its original clues, marks, notes and history before restoring it as practice. A saved completed board does not create a new score.

Do different seeds always produce different puzzles?

No. A seed deterministically controls original row construction and clue removal, but two seeds can produce equivalent solutions. The page tracks already opened solution identities across seeds, rotations, reflections and swapping 0 with 1; those attempts remain practice.

Can I print without revealing the answer?

Print puzzle prepares only the original clues and rules, excluding your entered marks and notes. Print puzzle and answer key explicitly adds a separate solution page and makes an unfinished challenge practice only. Opening the print dialog does not confirm that a PDF was saved.

Binairo Puzzles

Fill original binary grids with 0 and 1 while balancing every row and column, avoiding triples and keeping completed lines distinct. Generate a reproducible puzzle, add pencil notes, check the rules or print the clues. A fresh unassisted 6×6 solve can challenge someone to use fewer cell changes.

Original seeded binary puzzles · every offered board is verified unique

Choose a puzzle4 × 4, 6 × 6, 8 × 8

Board sizePuzzle seed

Seed: whole number from 0 to 4294967295.

Generation version 1 uses original deterministic row construction and clue removal. Every offered puzzle passes exhaustive uniqueness checking. A failed or exhausted search produces no board.

Rules and feedbackOnly on request

Balanced and different
Each completed row and column needs equal numbers of 0 and 1. Completed rows must differ from each other, and completed columns must differ from each other.

No triples
Three adjacent identical values are forbidden horizontally and vertically. Blank cells prevent completion.

The solver counts up to two completions and separates zero, unique, multiple and exhausted outcomes. A puzzle is playable only after exact uniqueness is proved.

Choose a size and seed, then generate an original puzzle.

Board: Not started

Status: Not started

Cell changes: 0

Solution count: Not verified

Worked rules

0 0 1 0 1 1Balanced row
Three of each value and no triple. The column and uniqueness rules still apply.
0 0 0 1 1 1Adjacent triples
Invalid. Both groups of three break the rule.
Two equal full rowsAll positions match
Invalid. Every completed row must differ.

Accuracy. Every completed row and column contains equal numbers of 0 and 1, has no three equal adjacent cells, and differs from every other completed row or column of the same orientation. Original seeded puzzles are offered only after bounded exhaustive solution counting proves exactly one solution; an exhausted search is not proof. Pencil notes do not change the board or count as scored cell changes.

Common questions

What are the rules of Binairo?: Each completed row and column contains equal numbers of 0 and 1. Three adjacent equal values are forbidden horizontally and vertically. No two completed rows may be identical, and no two completed columns may be identical. Blank cells prevent completion.
Are the puzzles uniquely solvable?: Every offered board is generated by the pinned version 1 algorithm and checked by a bounded exhaustive solver that counts up to two solutions. A board is published only when exactly one solution is proved. Failed, ambiguous or exhausted generation produces an error and retry option, not a playable board.
How do cell marks and pencil notes work?: Choose 0, 1 or Blank and activate a non-clue cell. The fixed clues have an underline. Enable Pencil notes to toggle tentative 0 or 1 notes in a blank cell; both can be shown. Notes do not fill the cell or count as scored changes. Arrow keys, Home and End navigate; 0, 1 and Backspace mark the focused cell.
What does Check current marks reveal?: It explains conflicts derived from your current marks: too many of one value, adjacent triples, and duplicate completed rows or columns. It does not compare every unfinished cell with the hidden answer. Requesting a check makes an unfinished challenge practice only.
How are challenge scores measured?: A challenge is one fresh 6×6 puzzle with no timer. Each successful explicit cell-state change counts, including corrections and blanking; lower is better. Clue clicks, unchanged marks, selections and pencil-only changes do not count. Checks, answers, undo, restored progress and previously opened equivalent puzzles disable scored sharing. Scores are self-reported.
Can I undo, redo or resume a puzzle?: Undo and redo restore recorded marks and notes. The browser can save your settings and puzzle progress locally. Resuming regenerates the seeded puzzle and validates its original clues, marks, notes and history before restoring it as practice. A saved completed board does not create a new score.
Do different seeds always produce different puzzles?: No. A seed deterministically controls original row construction and clue removal, but two seeds can produce equivalent solutions. The page tracks already opened solution identities across seeds, rotations, reflections and swapping 0 with 1; those attempts remain practice.
Can I print without revealing the answer?: Print puzzle prepares only the original clues and rules, excluding your entered marks and notes. Print puzzle and answer key explicitly adds a separate solution page and makes an unfinished challenge practice only. Opening the print dialog does not confirm that a PDF was saved.

Every completed row and column contains equal numbers of 0 and 1, has no three equal adjacent cells, and differs from every other completed row or column of the same orientation. Original seeded puzzles are offered only after bounded exhaustive solution counting proves exactly one solution; an exhausted search is not proof. Pencil notes do not change the board or count as scored cell changes.