Standard Binairo on a 6×6 board is a binary logic puzzle in which each row and each column contains three 0s and three 1s, no three identical digits sit side by side, and no two completed lines in the same direction repeat. Eight cells are pre-filled as immutable givens and the remaining 28 editable cells each hold one of three explicit working states: unknown, 0, or 1. The three rules apply at once, so a balanced line that copies another line or contains 000 is still illegal, and the puzzle is solvable only because the constraints interact. An independent enumeration of all 64 possible six-bit strings, filtered for balance and no-triple adjacency, leaves exactly 14 legal line patterns; the Lizely fixture selects six of those that together admit one and only one full grid. Working through that deterministic board is a compact way to practice every deduction family without designing a puzzle from scratch, and the same eight givens always appear in the same positions.
The Three Rules That Govern Every Binairo Cell
Every puzzle state can be checked against three independent rules that all have to hold at once. The first rule, often called balance, requires each row and each column to contain exactly three 0s and three 1s. The second rule, often called adjacency, forbids any run of three identical adjacent digits in any row or column, so sequences such as 000, 111, or longer are illegal. The third rule, often called uniqueness, requires that no two completed rows are identical and that no two completed columns are identical. The three rules interact in ways that hide deductions behind apparent shortcuts.
A row that already has three 0s in known cells must be filled with three 1s, even if the resulting line would copy another row — that copy is what forces uniqueness to reject the proposed digits somewhere else in the grid. Likewise, a column with a 0 in cells 2 and 3 forces cell 4 to be 1, even if placing 1 there pushes the column toward copying an already-finished column. Solving the grid means running all three checks together on every fill, not applying them in sequence.
How the 6×6 Puzzle Is Constructed and Proven Unique
The board starts with eight fixed givens that cannot be changed. They appear at row 1 column 1; row 2 column 6; row 3 columns 3 and 4; row 4 column 3; row 5 column 5; and row 6 columns 2 and 6. Each is rendered with a distinct visual treatment so you cannot mistake an editable cell for a starting digit. With 36 cells on the board and 8 givens, the solver decides 28 cells in total: 36 minus 8 leaves 28, with each of the six rows holding exactly three 1s and three 0s once complete.
Uniqueness is not assumed; it is mechanically proven. The grid is built by listing every six-bit string from 000000 to 111111, which gives 64 candidates, then keeping only those strings with three 0s, three 1s, and no run of three equal digits — the result is 14 legal row patterns. From those, the fixture selects six distinct rows that match the givens, then builds the grid column by column while rejecting any column prefix that violates balance or forms an equal triple. Once all six columns are complete, the search requires six distinct legal columns. The independent procedure returns exactly one grid for this clue set.
The eight clues are also tested individually. The search reruns with each given removed in turn and stops as soon as two solutions are found. Every removal admits more than one completion, which proves that every visible given contributes to uniqueness. None of the clues is decorative. The puzzle you play at Binairo (Binary Puzzle) is the result of that exact search, not a board borrowed from another source.
Solving the Board Step by Step
- Open Binairo (Binary Puzzle) and confirm the eight givens appear in the documented positions, with the first editable cell already selected.
- Scan every row and every column for cells that already contain three 0s or three 1s in known cells. Any remaining open cell in such a line is forced to the opposite digit by balance.
- Look for adjacent pairs of the same digit separated by an unknown cell. A pattern like 0 _ 0 forces the middle cell to 1; the same applies to 1 _ 1 forcing 0. Pairs at the edge of a row or column extend the rule outward to the third edge cell.
- For each row that already has five cells decided, check whether the sixth would copy another completed row. If it does, swap the last placed digit if the alternative still satisfies balance and adjacency.
- For each column that already has five cells decided, repeat the same uniqueness check against the other five completed columns.
- Fill any still-unknown cell with the only digit that satisfies balance, adjacency, and uniqueness simultaneously.
- Choose Check grid or press Enter. The unique completion returns exactly 1,000 points.
If any editable cell is still unknown when you check, the board is reported as incomplete and your mistake counter does not advance. That lets you inspect a half-finished attempt without penalty and resume the deduction from where you stopped.
Three Deduction Families and How to Combine Them
The three rules of Binairo give rise to three deduction families, and the order in which you apply them changes how quickly the board falls into place.
| Deduction | Pattern it exploits | What it forces |
|---|---|---|
| Balance | A line with three 0s or three 1s in known cells | Every other open cell in that line becomes the opposite digit |
| Adjacency | Two identical neighbours separated by an open cell or sitting at the edge | The middle cell, or the third edge cell, becomes the opposite digit |
| Uniqueness | A near-complete line that would copy an already-completed line | The last open digit must change, even when balance and adjacency allow the copy |
Balance deductions tend to arrive first because they only require counting known digits. Adjacency deductions arrive next, because they only require reading pairs of neighbours. Uniqueness deductions arrive last, because they require at least one completed line in the same direction to compare against. A useful habit is to scan each line in turn and stop at the first deduction that applies; jumping between rules often duplicates work. When two deductions disagree — for example, when adjacency suggests 0 but uniqueness suggests 1 — trust uniqueness, because the equal-triple ban only requires two copies of the digit, while uniqueness forbids a whole-line copy outright.
Keyboard and Touch Controls at a Glance
| Action | Touch or pointer | Keyboard |
|---|---|---|
| Move between cells | Tap an editable cell to select it | Arrow keys |
| Set a cell to 0 | Set 0 button after selecting a cell, or tap to cycle to 0 | 0 |
| Set a cell to 1 | Set 1 button after selecting a cell, or tap to cycle to 1 | 1 |
| Clear a cell back to unknown | Clear button or cycle past 1 | Delete or Backspace |
| Cycle unknown → 0 → 1 → unknown | Tap an editable cell repeatedly | Space |
| Check the full board | Check grid button | Enter |
Starting digits cannot be changed. The Clear button, the cycle tap, the Delete key, and the Space key all act only on the currently selected editable cell, so an accidental interaction with a given has no effect. The grid is laid out in six bounded columns with square cells that fit inside a 390-pixel viewport without horizontal scrolling, which keeps the same tap targets visible whether you are on a desktop or a narrow phone screen.
Scoring, Mistakes, and the Restart Rule
The grid is scored in whole points. An unfinished board that you check is reported as incomplete without advancing the mistake counter, so you can use Check grid as a planning tool while filling. A fully filled board that is wrong adds one mistake and stays editable, which lets you revise the cell that broke a rule. A second fully filled incorrect check deadlocks the run until you choose Restart, and Restart always reloads the same fixed puzzle with the same eight givens, all other cells cleared to unknown, the score reset to 0, and the first editable cell selected.
The unique correct grid awards exactly 1,000 points. Both completion and two-mistake deadlock are terminal states: after either one, the grid buttons, Set 0 and Set 1, the Clear button, the Check grid button, the keyboard edits, and the arrow keys stop changing game state. All puzzle logic runs locally in the browser, so nothing is sent to a server, no account is required, and no permission is asked for.
What a 1,000-Point Run Does and Doesn't Prove
Binairo is recreational logic practice, not a standardised cognitive test. The Lizely fixture is a single deterministic board that becomes familiar after repeated play, and a 1,000-point result only means that you completed this one puzzle under its declared rules. The score does not measure general intelligence, working memory, attention, educational readiness, or any medical or psychological trait. Treat it as a way to keep the three deduction families sharp — balance, adjacency, uniqueness — and as a way to audit each move against every rule at once.
The standard rule language itself is drawn from published references for Conceptis Tic-Tac-Logic rules and Puzzle Binairo; those sources define the three constraints used here but do not supply this board, score, interface, or mistake policy. Those are original product decisions, which is why an independent enumeration can find exactly one grid instead of inheriting a puzzle from elsewhere.
Related reading: How to Choose Your Next Step in the Four-Bit Binary Game.