Separate board size from the work inside it
An 8x8 grid has 64 cells and needs four zeros and four ones in every row and column. A 12x12 grid has 144 cells and needs six of each. The larger board gives you more cells to inspect. That extra scanning does not tell you which deduction will settle a stubborn blank.
Clue count tells you how much is filled at the start. Placement determines what those clues reveal. Two neighboring zeros can give an immediate one; scattered digits may leave several balanced line patterns to compare.
The useful question is what happens when the obvious moves run out. Can you finish by avoiding triples and filling a line's remaining quota, or must you compare whole candidates? Keep the usual solving routine nearby if those steps are new.
Board A reaches a shared candidate value
Both boards below have 36 fixed clues, 28 blanks, and exactly one solution. They even lead to the same completed grid. Each passed the current generator's Medium checks. Dots represent blanks, and coordinates count from the top left.
In Board A, the recorded solve makes 20 placements before reaching its candidate comparison. Row 6 then reads _ _ _ 1 0 0 1 0. Its only balanced, triple-free completions are 10110010 and 11010010. Both begin with 1, so step 21 places 1 at R6C1.
The next two cells still differ between the candidates. Leave them open until another deduction settles them. Finding one shared digit is enough to restart the simpler scans.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 0 | · | 1 | · | 1 | · |
| 2 | · | 0 | · | 0 | 1 | 1 | · | · |
| 3 | 1 | 0 | 0 | · | 0 | · | · | · |
| 4 | 0 | 1 | 0 | · | 1 | 0 | 1 | 1 |
| 5 | 1 | · | 1 | 0 | 0 | 1 | · | 1 |
| 6 | · | · | · | 1 | 0 | 0 | 1 | · |
| 7 | · | 1 | · | 0 | 1 | · | · | 1 |
| 8 | · | · | · | 1 | · | · | · | 0 |
Board B needs a completed row for comparison
Board B reaches a different obstacle after 24 placements. Row 2 still reads _ 0 1 0 _ 1 0 1. The two row candidates are 00101101 and 10100101. They disagree at both blanks, so neither blank has a shared value.
By then, row 5 is complete as 10100101. The classic rule requiring distinct rows excludes that candidate from row 2. Only 00101101 remains, so step 25 places 0 at R2C1. Balance fills R2C5 with 1 on the next step.
Both boards began with 36 clues, but their arrangements led to different deductions. Board A's key move came from the possibilities within one row. Board B also needed information from a completed row elsewhere in the grid.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
|---|---|---|---|---|---|---|---|---|
| 1 | 0 | · | 0 | · | · | · | 1 | 0 |
| 2 | · | 0 | 1 | 0 | · | 1 | 0 | 1 |
| 3 | 1 | 0 | 0 | · | 0 | · | · | 0 |
| 4 | 0 | · | 0 | · | 1 | 0 | · | 1 |
| 5 | · | · | 1 | 0 | 0 | 1 | · | 1 |
| 6 | · | 1 | 0 | 1 | · | 0 | · | · |
| 7 | 0 | · | · | 0 | · | · | 0 | · |
| 8 | 1 | · | · | 1 | · | 1 | 0 | · |
Read the measurements with their method attached
We froze sample set D06 v1 on October 13, 2026, using generator v2. After every placement, the analyzer checks no-three moves, then balance, line candidates, line uniqueness, and finally contradiction. One step means one filled cell. Independent enumeration confirmed each board's single solution.
The table records that particular scan order. It does not prove that every human must follow it, or that Board B will take longer. A player may notice several consequences together. The downloadable record includes both seeds, every move, and the grids before the key deductions.
| Measurement | Board A | Board B |
|---|---|---|
| Starting clues | 36 | 36 |
| No-three placements | 13 | 12 |
| Balance placements | 14 | 15 |
| Line-candidate placements | 1 | 0 |
| Line-uniqueness placements | 0 | 1 |
| Contradiction placements | 0 | 0 |
| Highest rule used | Line candidates | Line uniqueness |
| Total placements | 28 | 28 |
What our four binary puzzle difficulty levels accept
Our generator checks the strongest rule used and the number of advanced placements. Here, advanced means comparing line candidates, applying uniqueness, or ruling out a value by contradiction. Every accepted board must have one solution and a complete solve through the rule engine.
For 8x8 boards, the acceptance checks are below. Medium allows both sample profiles. Hard and Very hard also accept some of the same profiles, so a single uniqueness move does not determine the label. The generator additionally aims for different clue densities and preferred rule strengths when choosing a puzzle.
| Level | Measured solve must meet | Practice focus |
|---|---|---|
| Easy | Only no-three and balance | Spot local patterns and count quotas |
| Medium | Highest rule is line candidates or uniqueness | Compare whole line possibilities |
| Hard | At least two advanced placements, or any uniqueness or contradiction | Connect deductions across the board |
| Very hard | At least three candidate placements, or any uniqueness or contradiction | Stay with less immediate openings |
Why the same label can feel different elsewhere
There is a size-specific exception here. On 6x6 Medium, the analyzer accepts at least two rule families with no rule above uniqueness. A compact Medium board can therefore finish with no-three and balance alone.
Other publishers define their own settings. Simon Tatham's Unruly manual lists width, height, difficulty, and optional unique rows and columns separately. With that uniqueness option disabled, Board B's duplicate-row argument would be unavailable.
What makes Takuzu hard for you also depends on which patterns you recognize. Our labels describe the generator's checks. They provide no measured average solving time or universal ranking of players.
Choose a level for the deduction you want to learn
Keep the board at 8x8 while changing difficulty. Choose Easy to practice pairs and quotas, then try Medium when you want to compare candidate lines. A larger board is a separate choice when you want more cells to manage.
When you stall, use Hint and read the explanation before pressing Place. Look at the exact reason for that move. Had a row already reached its quota of zeros, or did another completed row rule out a candidate? That gives you something specific to practice on the next board.
The online practice link creates a fresh puzzle. To revisit these exact examples, copy the printed grids above or keep the downloaded record.
Sources and sample version
The sample record identifies the generator revision used for these measurements. The official rule pages below support the classic constraints and the Unruly settings comparison.