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Lizely

Binairo (Binary Puzzle)

Solve an original, uniquely determined 6 by 6 binary grid with standard Binairo rules, touch controls, full keyboard support, and exact scoring.

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How to use

  1. 1.Use the givens to enforce three 0s and three 1s in every row and column, with no 000 or 111 sequence.
  2. 2.Fill open cells by tapping to cycle, using Set 0 and Set 1, or pressing 0 and 1 while moving with the arrow keys.
  3. 3.Make every completed row and column unique, decide all 36 cells, then choose Check grid or press Enter for exactly 1,000 points.

About Binairo (Binary Puzzle)

Binairo is a compact binary logic puzzle played with only 0 and 1. This original six-by-six board begins with eight fixed digits. Fill every other cell so that each row and each column contains exactly three 0s and three 1s, no row or column contains three equal adjacent digits, and no two completed rows or completed columns are identical. All three conditions matter at the same time. A line can have balanced totals yet still be illegal because it contains 000, 111, or duplicates another line.

The grid uses three explicit working states. An open cell begins unknown, then can hold 0 or 1. Click or tap an editable cell to cycle from unknown to 0, from 0 to 1, and from 1 back to unknown. The separate Set 0, Set 1, and Clear buttons give direct control over the currently selected cell. Starting digits use a distinct visual treatment and cannot be changed. This separation prevents an accidental tap from corrupting the puzzle definition.

Balance is often the easiest deduction. If a six-cell line already contains three 0s, every remaining open cell in that line must be 1. The same reasoning applies after three 1s. Adjacency gives a second family of deductions. If two neighboring cells are both 0, the cell immediately before or after that pair, when present, must be 1. If a line shows 0, open, 0, the middle cell must be 1. Swap the digits and the same patterns apply.

Distinctness becomes useful later. Once five cells in a row are known, compare that partial row with completed rows. A final digit that would copy another completed row is forbidden even if balance and adjacency would otherwise allow it. Columns follow exactly the same rule. Distinct rows may equal columns because uniqueness is enforced within each direction, not across the two direction sets.

The published answer is an original Lizely fixture rather than a board copied from either reference. Its six rows are 001011, 001101, 110010, 010011, 101100, and 110100. Tests inspect every row and independently extract every column. Each line must contain three of each digit and no equal run longer than two. Separate set comparisons require six unique row encodings and six unique column encodings.

A correct answer is not enough if the starting digits allow several valid completions. The fixture therefore has a finite uniqueness proof. There are only 64 possible six-bit lines. An independent enumerator filters them directly by the balance and no-three-equal rules and finds 14 legal line patterns. It then chooses six distinct legal rows that match the givens, rejects any column prefix with too many of either digit or an equal triple, and finally requires six complete legal, distinct columns. That independent search finds exactly one full grid.

The clue set is deliberately small but auditable. Its eight givens 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. The test removes each given in turn and reruns its independent search with an early stop after two answers. Every removal admits more than one completion, showing that each displayed clue contributes to uniqueness rather than being decorative.

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. This 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 Restart. The unique correct grid awards exactly 1,000 points.

Completion and deadlock are terminal states. After either one, grid buttons, explicit value controls, checking, keyboard edits, and cursor movement no longer change game state. Restart creates a fresh copy of the same fixed puzzle with its eight givens, all other cells unknown, zero mistakes, zero score, and the first editable cell selected. The deterministic board makes results reproducible and keeps the evidence test stable.

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. The grid uses six bounded columns and 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, locally stored best score, Restart, and the double-Escape boss key. Press Escape twice within the shell timing window to cover the puzzle with the spreadsheet-style screen, then twice again to return. 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.

Conceptis Tic-Tac-Logic and Puzzle Binairo are cited for the standard rule language only: equal counts in every row and column, no three equal adjacent digits, and unique completed lines. They are not sources for this answer, starting layout, score, interface, mistake policy, or wording. Those are original product decisions, and the evidence package keeps that provenance boundary explicit.

Binairo is recreational logic practice, not a standardized test. The fixed board becomes familiar after repeated play, and a 1,000-point result only means this one deterministic puzzle was completed under these rules. It does not measure intelligence, attention, memory, educational readiness, or any medical or psychological trait. Use it to practice binary elimination and constraint checking, not to rank or diagnose people.

Methodology & sources

Define an original six-by-six binary answer and a separate eight-cell givens table. Verify every complete row and independently extracted column has three 0s, three 1s, and no run of three equal digits; encode lines and require six distinct rows and six distinct columns. Independently enumerate all 64 six-bit strings to obtain the 14 legal line patterns, then build the grid row by row while matching givens, forbidding duplicate rows, pruning column prefixes that exceed balance or form triples, and requiring six legal distinct columns at completion. Require one solution, and remove each given separately to prove every clue is necessary. Preserve explicit unknown, 0, and 1 states; ignore incomplete checks, allow one completed wrong grid to remain editable, deadlock after the second completed wrong check, award exactly 1,000 for the unique completion, and freeze all play input at either terminal state.

Frequently asked questions

What are the standard Binairo rules?
Each row and column must contain equal numbers of 0 and 1, may not contain three equal adjacent digits, and must differ from every other completed line in the same direction.
Will checking an unfinished grid count as a mistake?
No. If any editable cell remains unknown, the game reports an incomplete board and leaves the mistake count unchanged.
Does this board have exactly one solution?
Yes. An independent enumeration of legal six-bit rows and compatible column constraints finds exactly one completion, and each of the eight givens is necessary for uniqueness.
Can I play Binairo entirely with the keyboard?
Yes. Use arrows to move, 0 and 1 to fill, Delete to clear, Space to cycle states, and Enter to check.

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