How to play
Binary Puzzle(Takuzu)
Two numbers. One whole pattern.
Every blank has just two possibilities. Watch a rule cross one out, then follow what becomes certain.
A third zero would make 000.
Two together. Never three.
Fill every blank with 0 or 1. Two equal neighbours can sit together; three in a row cannot.
Try 0 in the third square. It would make 0, 0, 0. Cross that idea out: the square must be 1.
Dashed red: a candidate to rule out, not a placed digit.
Why must the third square be 1?
Choose an answer to check your reason.
Read the answer
Yes. The two zeros may touch. A third zero would make 000. Alternating is allowed, but is not required.
The solid digits stay. Dashed red digits are candidates being ruled out.
Look on both sides of a gap.
Keep that first row. Now look at row 3: 1, blank, 1.
Putting 1 in the gap makes three consecutive ones. The gap must be 0. A pair can constrain the space between it too.
Dashed red: a candidate to rule out, not a placed digit.
Only horizontal and vertical runs count. There are no diagonal rules.
Count what you know.
Every row and column needs equal numbers of zeros and ones: three of each on a 6 × 6, four of each on an 8 × 8.
Our first row has two zeros and two ones. The two blanks need one more of each. Counting alone has not told us where.
Can counting alone choose column 5?
Choose an answer to check your reason.
Read the answer
Exactly. Two of each are known. Balance asks for one more of each, without locating them. The pair of ones will choose column 5 next.
Small 0 / 1 marks mean unknown, not two numbers placed in one square.
Reach the quota. Then fill.
The pair of ones in columns 3–4 rules out another 1 in column 5. Put 0 there first.
Now count again: all three zeros are present. The last square must be 1. One rule made the next rule useful.
Dashed red: a candidate to rule out, not a placed digit.
Wait until a line has its full quota before filling every remaining blank with the opposite number.
Across and down, together.
Those same rows open into our whole 6 × 6. Every square belongs to a row and a column.
Balance and no triples work vertically too. There are no smaller boxes to fill. The underlined digits are the original fixed clues.
No Sudoku subboxes. Check the six whole rows and the six whole columns.
A perfect count can still fail.
Rows must all be different from other rows. Columns must all be different from other columns. A row may match a column.
Compare rows 1 and 5. Row 5 needs one more 0 and one more 1. Try 1, 0 in columns 4–5: every position would match row 1.
Can row 5 use 1, 0 in columns 4–5?
Choose an answer to check your reason.
Read the answer
Right. Every position would match row 1. Row 5 needs one 0 and one 1, so columns 4–5 must be 0, 1.
Dashed digits are an unplaced candidate. Row 5’s two blanks are still unknown.
Keep the difference.
Only two pairs have one 0 and one 1: 1, 0 or 0, 1. The first would duplicate row 1.
Cross out that pair. Put 0, 1 into row 5. Two different positions are enough: the rows do not need to be opposites.
Compare complete patterns, not just counts. The same rule applies to columns.
Let a small fact carry you.
Keep every proved digit. In row 2, the two ending zeros force a 1 just before them. That makes a 1, blank, 1 gap.
Follow the highlighted squares. Each run or reached quota gives one more certain value. Nothing here needs a guess.
Read each of these 5 moves
- R2 C4 = 1. Row 2 ends 0, 0. A 0 just before them makes three. Use 1.
- R2 C3 = 0. Row 2 has 1, blank, 1 in columns 2–4. Fill the gap with 0.
- R2 C1 = 1. Row 2 has three zeros. Its last blank must be 1.
- R3 C5 = 1. Row 3 has three zeros. Column 5 must be 1.
- R4 C3 = 0. Row 4 has 1, blank, 1 in columns 2–4. Fill the gap with 0.
Pause anywhere: the caption names the exact line and reason for the current move.
Turn your attention downwards.
Column 1 already has three ones. Its remaining blank must be 0. In column 2, three zeros force the last blank to 1.
That completes row 6’s quota of ones. Its other squares become zeros. Keep switching between rows and columns as each new digit helps.
Read each of these 7 moves
- R4 C1 = 0. Column 1 has three ones, in rows 2, 3 and 6. Row 4 must be 0.
- R6 C2 = 1. Column 2 has three zeros, in rows 1, 3 and 5. Row 6 must be 1.
- R6 C3 = 0. Row 6 has three ones. Column 3 must be 0.
- R6 C4 = 0. Row 6 still has all three ones. Column 4 must be 0.
- R6 C6 = 0. Row 6 still has all three ones. Column 6 must be 0.
- R4 C5 = 0. Column 5 has three ones, in rows 3, 5 and 6. Row 4 must be 0.
- R4 C6 = 1. Row 4 has three zeros. Its last blank must be 1.
Keep the three known ones in view. Each new digit gives its neighbours another fact.
Two numbers. One whole pattern.
Three of each, in every line. No three equal neighbours. Six different rows, six different columns.
The whole arrangement comes from those little proofs. Now try the same checks on a different puzzle.
The two-tone finish follows the proof. It never supplies a move.
Try a fresh patternA different puzzle.
Your next proof.
Start with the pair of ones in the first row. Then look for gaps, reached quotas and matching lines.
Practice lasts while this page is open. Your regular game and its local save stay separate.
17 / 36 filled6 × 6 · three of each
Make only a move you can explain. A mistake stays on the board so you can change it or undo.
Start this practice puzzle again? Your previous attempt can be restored with Undo.
Touch & keyboard controls
Select 0, 1 or Erase, then tap a square. Tap the same value again to clear it. There is no dragging, so you can scroll normally.
Tab enters the board; arrows move, Home/End reach the ends of a row. Press 0 or 1 to enter it, Delete/Backspace to clear. Enter/Space uses your selected action. Ctrl/Cmd+Z undoes; add Shift to redo. Tab leaves the board.
Explain a move checks your current choices. A hint marks this attempt as assisted, even before Apply. A contradiction asks you to change or undo a choice. A search limit is not proof that a move exists.
Your next pattern is waiting.
The empty spaces here are still unknown. Try the practice puzzle above, or take the three checks into a regular game.
Play Binary Puzzle Return to your practice6 × 6 and 8 × 8 · free · no account
Quick rules
- Fill every blank with 0 or 1. Underlined digits are fixed clues.
- Equal counts in every row and column. Three zeros and three ones in 6 × 6; four of each in 8 × 8.
- No three equal consecutive numbers. Across or down. Two may touch; diagonals do not matter.
- Different rows, different columns. No completed row may copy another row; no completed column may copy another column. A row may match a column.
Small questions
Must zeros and ones alternate?
No. Pairs such as 00 and 11 are allowed. Only runs of three or more are forbidden.
Are there Sudoku boxes?
No. Check whole rows and columns. There are no subboxes, sums or diagonal constraints.
When does balance force a move?
When a line has all three of one number on a 6 × 6, every remaining blank must be the other. Before then, counts may tell you how many are missing without locating them.
Does a row have to differ from a column?
No. Compare rows with rows and columns with columns. At least one different position is enough.
Where do these rules come from?
This guide follows this game’s engine and the BinaryPuzzle.com rules. Both guide puzzles are original; none was copied from that source. Board sizes are literal sizes, not difficulty ratings.