How to Solve a 6×6 Binary Puzzle, Step by Step

The quickest way to learn the binary puzzle isn't to reread the rules — it's to watch one get solved, one forced move at a time, with nothing skipped. So that's what this is: a complete walkthrough of a single 6×6 binary puzzle (also called Binairo or Takuzu), from the starting clues to the finished grid. The 6×6 is the smallest size, which makes it the perfect place to learn, big enough to use every core technique but small enough to follow every step. Grab a pencil and follow along, then play a 6×6 binary puzzle of your own. New to the rules? Our three-rules guide covers them first.

The puzzle

Here's our starting grid. Empty cells are shown as ·. We need to fill every cell with a 0 or 1 so that each row and column has three 0s and three 1s, no three identical digits sit in a row, and no two rows (or columns) end up identical.

	C1	C2	C3	C4	C5	C6
R1	0	1	·	1	1	·
R2	·	·	0	·	0	·
R3	0	·	1	·	·	·
R4	·	·	·	0	0	·
R5	1	1	·	·	·	·
R6	·	0	·	·	·	1

We'll refer to cells by Row and Column — so R2C3 is row 2, column 3.

Step 1: Pair forcing finishes row 1

Look at row 1: it has a 1 in C4 and a 1 in C5 — two 1s side by side. To avoid three 1s in a row, the cells on either end must be 0. So R1C3 = 0 and R1C6 = 0.

That completes row 1 as 0 1 0 1 1 0 — three 0s, three 1s. Pair forcing is the move you'll lean on most.

Step 2: A pair in row 5

Row 5 opens with 1 in C1 and 1 in C2 — another adjacent pair. The cell to their right, C3, must be 0 to stop a third 1. So R5C3 = 0.

Step 3: A pair in row 4

Row 4 has 0 in C4 and 0 in C5 — a pair of 0s. The cells on both ends must be 1: R4C3 = 1 and R4C6 = 1.

Step 4: The sandwich rule cracks row 2

Now row 2, which reads · · 0 · 0 ·. Notice C3 = 0 and C5 = 0, with a single gap at C4 between them. That's the sandwich pattern: a 0 in C4 would make three 0s in a row, so the gap must be the opposite. R2C4 = 1.

Step 5: Count completion fills a column

Time to switch from rows to columns. Look at column 3 with what we've placed: R1 = 0, R2 = 0, R3 = 1, R4 = 1, R5 = 0, and R6 still empty. That's already three 0s (R1, R2, R5). Since every column needs exactly three 0s and three 1s, the last empty cell can't be another 0 — so R6C3 = 1.

Step 6: A pair hiding in a column

Columns follow the no-three rule too. Look at column 4 from the top: R1 = 1, R2 = 1 (we placed that in step 4). Two 1s stacked — so the next cell down, R3C4, must be 0 to avoid three 1s vertically. R3C4 = 0.

Finishing the grid

From here, the same handful of techniques carry you home. Keep sweeping for adjacent pairs and sandwich gaps, complete any row or column that's hit its three-of-a-kind count, and — for the last stubborn cells — use the rule that no two rows or columns may be identical. Worked all the way through, the puzzle resolves to:

	C1	C2	C3	C4	C5	C6
R1	0	1	0	1	1	0
R2	1	0	0	1	0	1
R3	0	1	1	0	1	0
R4	1	0	1	0	0	1
R5	1	1	0	1	0	0
R6	0	0	1	0	1	1

Run a few checks against it: every row and column has exactly three 0s and three 1s, no line has three identical digits in a row, and no two rows (or columns) match. Every rule holds.

What you just learned

Notice the rhythm of the solve: pair forcing for the obvious moves, the sandwich rule for the hidden gaps, and count completion to finish lines — sweeping rows and columns the whole way. That's the exact toolkit you'll use on every binary puzzle, at any size. The bigger 8×8, 10×10, and 14×14 grids just have more steps, not different ones.

The only way to make it stick is to do it yourself. Play a 6×6 binary puzzle now, start by hunting for adjacent pairs, and watch the grid fall into place. When you're ready for more, our full solving techniques guide covers every move in depth.