Binairo is a binary logic puzzle played with only 0 and 1 on a fixed 6 by 6 grid that begins with eight given digits. The reader fills the remaining 28 cells so every completed row and every completed column contains exactly three 0s and three 1s, never contains three equal adjacent digits, and never duplicates another completed line within its own direction. Each line is checked independently, which is why a row can be balanced and free of equal triples and still be illegal if it copies another completed row in the same direction. The original board on Binairo (Binary Puzzle) exposes three explicit working states — unknown, 0, and 1 — so a player never has to guess between empty and zero, since unknown is its own cell state until it is explicitly set, cleared, or cycled. All puzzle logic runs locally in the browser, the score is exactly 1,000 for the unique correct grid, and the published answer is an original fixture with a finite uniqueness proof rather than a copied board.
Binairo Rules in Plain English
The standard Binairo rule set, as defined by Conceptis Tic-Tac-Logic and Puzzle Binairo, has three parts and all three apply at the same time.
- Balance. Each row and each column must contain equal numbers of 0 and 1. On a six-cell line that means exactly three of each.
- No equal triple. No row and no column may contain three identical digits in a row, which rules out both 000 and 111 as adjacent substrings.
- Uniqueness within direction. No two completed rows may be identical, and no two completed columns may be identical. Distinct rows may equal distinct columns because the uniqueness rule applies within each direction set separately.
Those three constraints interact. A line can be balanced, free of equal triples, and still be illegal because it duplicates another completed line within its direction. The puzzle is finished only when all 36 cells are decided, every row passes all three checks, and every column passes all three checks independently. Balance, adjacency, and distinctness are enforced by the same scoring pass, so a partial line that satisfies two of the three rules is still incomplete.
The 6 by 6 Board and Its Eight Givens
The puzzle ships as a single deterministic six-by-six board so every run begins from the same starting position. Eight cells are pre-filled and visually marked as starting digits that cannot be changed, which protects the puzzle definition from an accidental tap or keystroke. On the published board those givens sit 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.
The eight clues are deliberately small but auditable. Removing any single given and re-running an independent legal-line search produces more than one valid completion, which shows that every displayed clue contributes to uniqueness rather than being decorative. The same independent search finds exactly one full grid when all eight givens are present, which is why a correct answer is worth exactly 1,000 points. Because the board never changes, results are reproducible across sessions and the evidence package stays stable, which matters for anyone who wants to verify the uniqueness proof rather than trust it.
How to Solve a Binairo Puzzle
- Read the three constraints together. Before placing anything, look at the eight givens and check balance, no-equal-triple, and uniqueness for every partial row and column they touch.
- Force balance first. If a line already contains three 0s, every remaining open cell in that line must be 1. The same reasoning applies in reverse once three 1s are placed, so balance deductions are usually the cheapest moves available.
- Apply the adjacency rule. When two neighboring editable cells are both 0, the cell immediately before or after that pair — when present — must be 1. A pattern of 0, open, 0 forces the middle cell to be 1, and the mirror rule holds for two adjacent 1s anywhere in a row or column.
- Fill open cells by tap or key. Click or tap an editable cell to cycle from unknown to 0, from 0 to 1, and from 1 back to unknown. Use the dedicated Set 0, Set 1, and Clear buttons for direct control over the currently selected cell, or move with the arrow keys and press 0 or 1 to fill the selected cell.
- Use distinctness late. Once five cells of a row are known, compare that partial row with completed rows. A final digit that would copy another completed row is forbidden even when balance and adjacency would otherwise allow it. Apply the same comparison inside the column set.
- Check the grid. When all 36 cells are decided, choose Check grid or press Enter. A unique correct grid awards exactly 1,000 points and locks the run.
Three Deduction Families You Will Use
| Deduction | What it reads | What it forces |
|---|---|---|
| Balance | Counts of 0 and 1 already placed in a line | If three 0s are placed, every remaining cell in that line must be 1, and the same applies once three 1s appear |
| Adjacency | Two equal neighbors like 0, open, 0 or 1, open, 1 | The middle cell must take the opposite digit to prevent three equal adjacent digits |
| Distinctness | Five known cells in a near-complete line | The last cell cannot copy another completed row or column even if balance and adjacency would allow it |
Balance is usually the easiest first pass because the line length is only six, so a single move can finish a row once three of one digit are placed. Adjacency is the second family and is most useful once a few cells are settled, because it forces a digit the moment a pair appears. Distinctness becomes valuable toward the end of the puzzle when most of a line is known and the final digit is the only way to keep that row different from every other completed row, or that column different from every other completed column.
Checking, Mistakes, and the 1,000-Point Score
Checking has a clear two-strike contract. If any editable cell is still unknown, Check grid reports that the board is incomplete and does not increase the mistake counter, which lets you inspect an unfinished attempt without penalty. A fully filled but incorrect board records one mistake and remains editable so you can revise a deduction. A second fully filled incorrect check deadlocks the run until you press Restart, which creates a fresh copy of the same fixed puzzle with its eight givens, all other cells unknown, zero mistakes, and zero score.
The unique correct grid awards exactly 1,000 points. Completion and deadlock are both terminal states. After either one, grid buttons, explicit value controls, checking, keyboard edits, and cursor movement no longer change game state, so the run is preserved and a fresh Restart is the only way to begin again. The locally stored best score lives in the shared game shell alongside the visible score, so practice runs remain comparable across sessions on the same browser.
Keyboard, Touch, and Privacy
Keyboard controls mirror touch controls. Use the arrow keys to move around the six-by-six grid, press 0 or 1 to set the selected editable cell, Delete or Backspace to clear it, Space to cycle its three states, and Enter to check. Each cell is a native button with a row, column, and state label, and the grid uses six bounded columns with square cells inside a narrow maximum width so it fits a 390-pixel viewport without horizontal scrolling. The shared game shell supplies the visible score, a locally stored best score, Restart, and a double-Escape boss key that covers the puzzle with a spreadsheet-style screen and then twice again returns to it.
All puzzle logic runs locally in the browser. The game sends no moves or answers to a server, requires no account, uploads nothing, asks for no device permission, and adds no package dependency, so the deterministic board stays reproducible and the evidence package stays stable across runs. Practice sessions therefore depend only on the local copy of the fixture, which is one reason the puzzle reads as logic practice rather than as a scored assessment.