How to play Binary
A square grid with a few pieces already in place: solid discs and rings, the ones and zeros of the name. Fill every empty cell with one or the other until each row and each column holds exactly as many of each, with never three alike in a row.
Boards come in three sizes, 6 × 6, 10 × 10 and 14 × 14, each generated in your browser with exactly one answer that you can reach without guessing. The small board lasts a coffee; the large one has about 150 cells to fill.
Rules
- Every cell gets a solid disc (a one) or a ring (a zero).
- No more than two alike may sit next to each other across or down: three solids or three rings in a line are never allowed.
- Each row and each column holds as many solids as rings: three of each on 6 × 6, five on 10 × 10, seven on 14 × 14.
- No two rows may be the same, and no two columns.
- The pieces you start with sit in shaded cells and can’t be changed.
- Three alike in a row turn red, and a line with too many of one kind, or one that copies another, is tinted red. The clock stops when the last cell completes the board. Each size remembers its own board, and the clock pauses while the tab is hidden.
Controls
- Click / tap a cell
- Empty → solid → ring → empty
- Right-click / long-press
- The same, the other way round
- Drag
- Paint the same piece along a row or column
- Arrows / WASD
- Move the cursor
- 1 / 0
- A solid / a ring under the cursor (press again to take it away)
- Space / Enter
- Cycle the cell under the cursor
- Backspace / Delete
- Empty the cell
- C
- Toggle counts (what each row and column still needs)
- Z / Ctrl+Z
- Undo
- P
- Pause
Tips
- Look for pairs first. Two alike side by side need the other kind at both ends, so two solids are always flanked by rings.
- Then gaps. Two alike with one empty cell between them need the other kind in the gap.
- Count. Once a row has all its solids, every empty cell left in it is a ring, and the other way round.
- When a line needs just one more of a kind, try it in each empty cell in turn. Wherever it would force three of the other kind together, it can’t go.
- Counts (C) puts what each row and column still needs beside the board, which makes the late game quicker to read.
Binary strategy
Pairs and gaps first
Most of a board falls to two patterns. Two alike side by side push the other kind onto both ends; two alike with a gap push the other kind into the gap. Sweep every row and every column for both before you think harder, and sweep again around each new piece, since every placement can make a new pair.
Finish lines by counting
A line that has all its solids gets rings everywhere else, and the other way round. On the larger boards turn on counts (C): a line one piece from done stands out, and so does one that has slipped over half.
The last one of a kind
When a line needs one more solid and several rings, the solid can’t go just anywhere. Put it in each free cell in your head: if that leaves three free cells side by side, they would all be rings, so it can’t go there. Often only one cell survives, or some cell is a ring in every case. Every 10 × 10 needs this somewhere, since the generator only keeps boards where pairs, gaps and counts stall.
Two left of a kind
The same test works with two to place: try the ways the pair could go and keep only what every surviving arrangement agrees on. It sounds slow, but most placements fail at a glance because they would strand three of the other kind together.
No two lines alike
When a line has just two empty cells, one for each kind, compare it with the full lines running the same way. If one way of finishing it would copy a full line, it has to be the other way round. Every 14 × 14 board needs this or the two-left test somewhere.
About Binary
The puzzle goes by many names: Takuzu, Binairo, Binero, Binoxxo, Tic-Tac-Logic, Tohu-Wa-Vohu or simply binary puzzle. Some versions print 0s and 1s, others Xs and Os or black and white circles. Here they are rings and solid discs, so the board reads the same in either theme and needs no colour at all.
The generator here deals a random full grid that keeps every rule, then takes pieces away one at a time, keeping each removal only while a solver can still finish the board by reasoning alone. That also proves the answer is unique. The 6 × 6 falls to pairs, gaps and counting. A 10 × 10 is kept only if, somewhere, those stall and a line with one piece of a kind left needs a closer look, and on a 14 × 14 even that stalls somewhere, so you need a line with two left, or the rule that no two lines are alike.
Questions
Can I always solve it without guessing?
Yes. Every board was solved by reasoning before you saw it. The hardest steps are of the “if the last solid went here, three rings would end up together” kind.
Why discs and rings instead of 0 and 1?
They are the ones and zeros: a solid disc is a one, a ring a zero, and the keys 1 and 0 place them. Shapes are quicker to tell apart at a glance than digits, and they need no colour.
Why is a whole row tinted red?
It holds more than half of one kind, or it is full and exactly the same as another row. Columns work the same way.
What do counts do?
They show, beside each row and below each column, how many solids and rings it still needs. They only change the display, and your times count either way.
Is my board saved if I leave?
Yes, in your browser, one board per size. The clock pauses while the tab is hidden.
