Daily Binary Puzzle

Binary Puzzle is a constraint puzzle with three rules

A Binary Puzzle, often called Takuzu, uses only 0 and 1, but the small symbol set does not make it a guessing game. Every decision must satisfy three simultaneous constraints. Each completed row and column contains an equal number of zeros and ones. No row or column may contain three identical adjacent values. Finally, no completed row may be identical to another completed row, and no completed column may be identical to another completed column. The interaction is simple enough for a phone while the deductions become substantially richer on larger boards.

Balance is the first source of forced moves

On an 8×8 board every row and column must finish with four zeros and four ones. If a row already contains four zeros, every remaining empty square in that row must be one. The same idea works on 6×6, 10×10 and 12×12 boards with three, five and six of each value respectively. Because the count rule applies in both directions, one placement can complete a row count and immediately force a column count somewhere else.

Pairs force the value on either side

The no-three-identical rule creates compact local deductions. If two adjacent squares are both zero, an empty square directly before or after that pair must be one. If a pattern is zero, blank, zero, the middle square must be one. The same logic works for ones and works vertically as well as horizontally. These pair patterns are useful early because they do not require the rest of the row or column to be nearly complete.

Unique rows and columns matter near the finish

Completed lines must not duplicate each other. Suppose a nearly complete row matches another finished row in every known position except one. The final blank cannot take the value that would make the two rows identical, even if both values would satisfy the simple balance count. The same rule applies to columns. This is why a correct Binary Puzzle engine must check line identity instead of treating the game as only a count-and-triples exercise.

Four board sizes change the amount of planning

V0.96 includes 6×6, 8×8, 10×10 and 12×12 boards. The smallest size is useful for learning the rules and spotting pair deductions quickly. Eight by eight gives a compact full puzzle. Ten and twelve require more cross-checking because a placement can remain locally plausible for longer before the row-count or uniqueness rules force a conclusion. All sizes use the same rules rather than changing the meaning of the puzzle.

Easy, Medium and Hard are separate frozen pools

Each size has Easy, Medium and Hard source puzzles. Difficulty is represented by the amount of starting information and the resulting deduction path, not by changing the basic rules. The release freezes four source puzzles for every size and difficulty combination, creating forty-eight source puzzles before symmetry is applied. Practice then chooses deterministically from the relevant pool so an exact URL seed is replayable.

Every shipped source has one independently counted solution

The application does not label a puzzle unique merely because its bundled answer fits. A separate verifier enumerates legal row patterns and backtracks through the column constraints without using the browser application answer path. Each of the forty-eight sources is counted to exactly one solution. The verifier also confirms that the unique solution it finds matches the frozen solution stored with that source.

Eight symmetry variants expand replay without changing logic

A square Binary Puzzle can be rotated and reflected while preserving every rule. V0.96 uses eight geometric transforms for each frozen source. That creates three hundred eighty-four playable transformed boards. The independent verifier solves every transformed board and compares it with the correspondingly transformed frozen solution, so a symmetry transform cannot silently corrupt the clue or answer mapping.

Practice is deterministic after the URL seed is fixed

When Practice opens without an s parameter, the page writes a local seed into the URL. That seed selects the source puzzle and symmetry variant for the requested size and difficulty. Reopening the same seed identifies the same puzzle, while Fresh Practice creates another seed. This gives reproducible QA and useful sharing without creating an indexed page for every generated board.

Daily Binary Puzzle is date-stable and specialist-only

The Daily mode derives its board size, difficulty, source and symmetry from the calendar date. Its completion history and streak live under Binary Puzzle specialist stats. It does not insert Binary Puzzle into the frozen Today’s 6 rotation, does not change the platform Daily Score, and does not fabricate a network-wide daily leaderboard.

Hint and Check have different jobs

Hint fills one currently empty cell from the independently verified solution and marks the run Assisted. Check does not reveal a complete answer; it highlights rule conflicts such as too many of one value, a run of three identical values, or a duplicated completed line. That separation lets a player ask whether the current board violates a rule without being handed every remaining placement.

Undo and Redo restore the exact player state

Undo and Redo restore the grid, move count and assistance state around a real player action. Temporary conflicts are valid player-input states and are restorable. A browser QA pass caught an earlier restore rule that rejected conflicted boards; the contract was corrected so restoration validates data shape and immutable givens rather than requiring every intermediate player state to already satisfy the puzzle.

Autosave belongs to the exact puzzle identity

Practice autosaves by size, difficulty and seed. Daily autosaves by date. Returning to the same identity restores the player grid and move count instead of silently starting a different board. Starting information remains immutable: an autosave cannot replace or alter a given clue. The stored state is browser-local and does not imply cloud sync or an account.

Clean and Assisted results are kept separate

Hint, Undo, Redo and Restart are useful learning tools, but using them changes what information was available when a decision was made. The run therefore becomes Assisted. The specialist keeps clean solves separate so a help-assisted completion cannot quietly replace a clean best. Check also marks the run Assisted because it evaluates the player’s current work.

The product avoids fabricated status metrics

Binary Puzzle stores factual browser-local counts such as puzzles solved, clean solves, a best result for a size and difficulty, and specialist Daily history. It does not invent an IQ score, percentile, global rank, active-player count or server opponent. There is also no wagering, chips, prizes, purchases or paid randomness; the puzzle bank is local and deterministic.

A practical solving rhythm is local first, global second

Start with obvious pairs and balance counts because those usually create the cheapest forced cells. After each placement, scan both its row and column. When the board becomes denser, compare nearly completed rows and columns against finished lines to apply the uniqueness rule. If you are stuck, looking for a line with only two empty cells often exposes a count or anti-triple deduction before a Hint is necessary.