A Binairo (binary puzzle) puzzle example is a 6×6 grid filled with 0s and 1s in which every row and column contains three of each digit, no 000 or 111 appears, no two rows are identical, and no two columns are identical. Balance alone is not enough, because a line can contain three 0s and three 1s while still violating the adjacency or uniqueness rule.
The example below is the original fixed puzzle used by Binairo (Binary Puzzle). It begins with eight immutable digits and leaves every other cell explicitly unknown. Conceptis’s Tic-Tac-Logic rules describe the same standard rule family, but that reference is not the source of this particular grid or answer.
A ready-to-solve 6×6 example
In the grid below, X means unknown and bold digits are fixed givens. Rows are numbered from top to bottom and columns from left to right. The interactive game opens this same puzzle with the same eight givens and all other cells unknown.
| Row | Column 1 | Column 2 | Column 3 | Column 4 | Column 5 | Column 6 |
|---|---|---|---|---|---|---|
| 1 | 0 | X | X | X | X | X |
| 2 | X | X | X | X | X | 1 |
| 3 | X | X | 0 | 0 | X | X |
| 4 | X | X | 0 | X | X | X |
| 5 | X | X | X | X | 0 | X |
| 6 | X | 1 | X | X | X | 0 |
The fixed digits cannot be changed, which protects the puzzle definition from accidental edits. A proposed solution must satisfy all three constraints in every row and column. Uniqueness is checked separately for rows and for columns, so a row is allowed to have the same digit sequence as a column.
Three rules shown through short examples
These compact patterns illustrate the decisions that commonly move a Binairo grid forward.
| Pattern or scenario | Rule lesson |
|---|---|
| 0 X 0 | The unknown middle cell must be 1; otherwise there would be 000. |
| X X 0 0 X X | The open cells immediately before and after the 00 pair must both be 1. |
| 001011 | This is a legal six-digit line: it has three 0s, three 1s, and no equal triple. |
| 000111 | This line is illegal despite its balanced totals because it contains 000 and 111. |
| Two completed rows both equal 001011 | That pair of rows is illegal because completed rows must be unique. |
Balance 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 are known. This often resolves several cells at once, although it does not determine their order by itself.
Adjacency deduction: When two neighboring cells are both 0, the cell immediately before or after the pair, when present, must be 1. The 0 X 0 pattern is the same rule viewed from the middle. Swap the digits and the identical deductions apply to pairs and sandwiches of 1s.
Uniqueness deduction: Once five cells in a row are known, compare that partial row with the other completed rows. If its final digit would create a duplicate, that digit is forbidden even when balance and adjacency would allow it. Columns follow the same process, but rows are only compared with rows and columns only with columns.
Work through deductions from the givens
The starting grid supports several transparent deductions without requiring a guess. These examples show how local information combines with the whole-grid constraints.
- Inspect row 3. It reads X X 0 0 X X. Because columns 3 and 4 form a 00 pair, row 3 column 2 and row 3 column 5 must both be 1. Putting a 0 in either location would create 000.
- Transfer the pattern to column 3. Column 3 reads X X 0 0 X X because row 3 column 3 and row 4 column 3 are fixed zeros. The same adjacency rule therefore sets row 2 column 3 and row 5 column 3 to 1.
- Update row 3. Its pattern is now X 1 0 0 1 X. It contains two 0s and two 1s, so balance requires the two remaining cells to contain one 0 and one 1. Balance does not reveal which cell gets which digit.
- Use uniqueness later. One local ordering of row 3 would make it 010011. After row 4 resolves to that same sequence, however, two identical rows would violate uniqueness, so that ordering is rejected. The surviving row 3 is 110010.
This sequence illustrates an important solving habit: record what a rule forces, but leave a cell unknown when the available evidence does not determine it. A correct Binairo answer comes from satisfying every line simultaneously, not from choosing the most plausible-looking option.
Solve the example in the interactive grid
The supported workflow accommodates both pointer and keyboard play while preserving unknown, 0, and 1 as separate states.
- Open the fixed board. Identify the eight starting digits before entering anything. They are visually distinct and cannot be edited.
- Scan rows and columns together. Look for a forced balance, an equal pair, or a five-cell line that can be compared with a completed line.
- Enter values by touch or pointer. Clicking or tapping an editable cell cycles it from unknown to 0, from 0 to 1, and from 1 back to unknown. Set 0 and Set 1 assign a value directly, while Clear returns the selected cell to unknown.
- Use the full keyboard route. Move with the arrow keys, press 0 or 1 to fill the selected editable cell, press Delete or Backspace to clear it, press Space to cycle its three states, and press Enter to check the grid.
- Decide all 36 cells. Do not leave an ambiguous cell unknown merely because one rule suggests a value. Confirm every row and column against balance, adjacency, and uniqueness.
- Check only when the grid is complete. Choose Check grid or press Enter. An unfinished board is reported as incomplete and does not increase the mistake counter, so it can be inspected without penalty.
- Respond to the result. A correct unique grid awards exactly 1,000 points. A fully filled but incorrect grid records one mistake and remains editable. A second fully filled incorrect check deadlocks the run until Restart is used.
Reference answer and independent verification
If you want to compare a completed attempt rather than solve from the givens, the unique reference grid is:
- 001011
- 001101
- 110010
- 010011
- 101100
- 110100
Reading the columns from top to bottom gives the same six sequences in the same order. This is permitted because uniqueness applies within the row set and within the column set, not between the two sets. Every row and every independently extracted column contains three 0s, three 1s, and no run of three equal digits. The six row encodings are unique, and the six column encodings are unique.
A visible answer alone cannot prove uniqueness, but this fixture has a separate verification. An independent enumerator checked all 64 possible six-bit lines, retained 14 patterns that satisfy balance and the no-three-equal rule, and searched for a complete grid matching the givens and distinct-column requirement. It found exactly one completion. Removing each of the eight givens separately allowed more than one completion, confirming that every displayed clue contributes to uniqueness.
Scoring and mistake limits
The documented completion award is a fixed 1,000 points, not a partial-point or time-based formula. Checking an incomplete board is harmless because it leaves the mistake count unchanged. The first fully filled incorrect submission costs one mistake but leaves the grid editable for correction.
A second fully filled incorrect submission deadlocks the run. Completion and deadlock are both terminal states: grid buttons, value controls, checking, keyboard edits, and cursor movement no longer alter the game. Restart creates a fresh copy of the same fixed puzzle with eight givens, all other cells unknown, zero mistakes, and zero score. Puzzle logic runs locally in the browser and requires no account or uploads.
How to use puzzle examples effectively
Treat an example as a constraint-checking exercise: first satisfy the givens, then test each row and column independently, and only reveal the reference answer after every cell has been decided. For additional paper practice, the printable 6×6 Binairo alternative provides another route to the same grid format.
A 1,000-point result means that this one deterministic puzzle was completed correctly. The fixed board becomes familiar after repeated play, so the score is not a standardized measure of intelligence, attention, memory, educational readiness, or any medical or psychological trait. Binairo is recreational logic practice, not a diagnostic test.
Related reading: How Do I Improve After a Failed Four-Bit Binary Game?.