Takuzu Strategy: The Binary Grid, Solved

Updated June 2026

Takuzu — also sold as Binairo, Unruly, or simply binary puzzle — fills a grid with only two symbols, usually 0 and 1. With just three rules it manages to be genuinely tricky, but every one of those rules is a ready-made deduction. Learn the four techniques below and you will fill the grid in a steady stream of forced moves.

The three rules

• No three in a row. You may never have three identical symbols next to each other, horizontally or vertically. Pairs are fine; triples are forbidden.
• Balanced lines. Every row and every column contains an equal number of 0s and 1s. On a grid of width 10, that means exactly five of each per line.
• All lines unique. No two rows may be identical, and no two columns may be identical.

Technique 1: Avoid the triple

This is where most cells get filled. The no-three rule works in two directions:

• Two the same, flanked. If you see two identical symbols side by side, the cells on both ends must be the opposite symbol — otherwise you would make a triple. So 1 1 with empty neighbours forces a 0 before and after it.
• The gap between a split pair. If two identical symbols sit with a single empty cell between them, that middle cell must be the opposite symbol. 0 _ 0 cannot be filled with a 0 (that makes three), so the middle is a 1.

Sweep the whole grid for these two patterns first; they cost no thought and trigger chain reactions.

Technique 2: Complete the count

Because each line holds an equal split, you finish a line the moment one symbol is used up. On a width-10 row that already contains five 1s, every remaining empty cell must be a 0 — there is no room for another 1. Always glance at a line's running tally; lines that are one or two short of half are usually completable in a single stroke, and completing them feeds new "avoid the triple" deductions into the crossing lines.

Technique 3: Prevent the forced triple

This one is subtler and breaks open the harder boards. Sometimes a cell is not forced by what is next to it, but by what would happen to a line's balance otherwise. Suppose a row needs two more 0s and two more 1s across four empty cells, and three of those cells form a run where placing a particular symbol would unavoidably create a triple somewhere down the line. Then the only legal distribution forces specific cells. The practical version: whenever filling a cell one way would leave the rest of the line unable to avoid a triple while staying balanced, fill it the other way.

Technique 4: Use line uniqueness to finish

Late in a solve, the "no two identical lines" rule resolves the last ambiguous cells. If a row is complete except for two empty cells, and another row in the grid is already fully filled, then your row may not end up identical to that one. If one of the two ways to fill your row would duplicate the finished row, the other way is forced. This technique rarely starts a board, but it reliably closes out the final few cells that the other rules leave balanced two ways.

A reliable order of attack

1. Scan for pairs and split-pairs and apply "avoid the triple" everywhere.
2. Complete any line that has hit its quota of one symbol.
3. Re-scan the crossing lines — each filled cell creates new triple-avoidance moves.
4. When stuck, look for cells where one choice dooms the line's balance, and take the other.
5. Finish ambiguous lines with the uniqueness rule.

Every Takuzu board has one solution reachable without guessing. If you ever feel like flipping a coin, re-scan for a split pair or a line that is one symbol from its quota — the forced move is almost always hiding in plain sight.