Pair cap
Two matching neighbors force the open cell beside them to the opposite digit.
BINARY PUZZLE · TAKUZU · EXACT PROGRESSION
Binary Puzzle
Prove every 0 and 1 across a 90-level campaign. Daily and seeded Practice stay repeatable, while verified hints explain one forced next move from the current state instead of exposing the full answer.
ModeCampaign
Level1 / 90
Grid6×6
RunClean
Every row and column balances 0 and 1.
6×6–12×12 can fall back to exact continuation proof. 14×14 deliberately stays on the fast named-deduction chain rather than pretending an expensive answer reveal is a logical hint.
Advanced V0.230 Logic Lens · 60 frozen sources · candidate analysis · print/share
BINARY PUZZLE · TAKUZU · VERIFIED DEDUCTION
Binary Puzzle prove every 0 and 1
Fill the grid without guessing. The V0.230 Logic Lens explains named deductions, checks the exact constraint model on demand, and keeps help-assisted runs separate from clean solves.
Moves0
Practice Binary PuzzleDeterministic once the URL seed is fixed.
CleanFilled —Time 0:00
Every row and column has an equal number of 0s and 1s.
Binary Puzzle
V0.230 LOGIC LENS
Local proofSee why the next move is forced
The live lens uses only the three Binary Puzzle rules for local deductions. “Verify state” additionally runs the independent full constraint model and reports whether the current entries still admit the unique board.
Row candidates—
Column candidates—
Forced cells—
Exact solutionsNot checked
Scan ready
The next named deduction will appear here without pretending an answer reveal is a logical hint.
Solved0
Clean solved0
Best this level—
Daily streak0
REPEATABILITY
No hints used yet.Recent solves and technique evidence
No completed runs on this device yet.
BALANCE
Use an equal number of 0s and 1s
Every row and column contains exactly half zeros and half ones. Once a line reaches its quota, every remaining cell is forced to the other value.
PAIRS & SANDWICHES
Stop triples before they form
00_ and _00 force a 1 at the open end. A pattern such as 0_0 forces a 1 in the gap. The Logic Lens names both deductions rather than exposing an answer cell.
UNIQUE LINES
Compare legal line completions
No two completed rows or columns can match. V0.230 enumerates every balanced, no-triple completion of a line and can prove when uniqueness removes the last alternative.
VERIFIED BANK
60 frozen sources, now through 14×14
The bank spans 6×6, 8×8, 10×10, 12×12 and 14×14 at Easy, Medium and Hard. Every source and all eight geometric symmetries are independently rechecked before sealing.
CLEAN VS ASSISTED
Learning help never masquerades as clean
Verified Hint, state verification, candidate marks, Check, Undo, Redo and Restart mark the run Assisted. Color mode and keyboard controls do not.
LOCAL FIRST
Daily archive, autosave and history stay here
Date-stable Daily puzzles, Practice seeds, recent runs, bests and streaks remain browser-local. No account, ranking fiction, paid API or remote gameplay dependency is required.
Sandwich
Matching digits with one gap force the gap to the opposite digit.
Balance completion
When a row or column reaches its quota, every remaining cell flips to the other value.
Unique-line prevention
Rule-valid line completions that would duplicate a completed line are removed.
Line consensus
If every legal completion of a line agrees on a cell, that cell is forced.