Binairo (Takuzu) — Binary Puzzle

Binairo is a logic puzzle of zeros and ones. You will also find it as Takuzu, as the binary puzzle, or as binary sudoku. The grid is square, a few digits are given, and you fill every empty cell with a 0 or a 1. Nothing is hidden and nothing is left to luck: every given digit is a fact, and a fair puzzle has one finished grid.

The three rules are the whole game. After the rules, this page covers the controls on the site and the first patterns worth learning by name.

Rules

Every cell holds a 0 or a 1. The given digits never change.

No three in a row. At most two equal digits may sit next to each other, horizontally or vertically. A row may contain 0 0 1, but never 0 0 0.

Every line is balanced. Each row and each column contains as many 0s as 1s, so a row of 8 cells has four of each.

No two lines are alike. Two finished rows may not be identical, and two finished columns may not be identical.

Each puzzle here has one solution. If two different finished grids both obeyed the rules, the binary puzzle would not be fair.

How to play on this site

Opening Binairo loads today’s daily puzzle, an 8×8 easy grid. The seed is the UTC date, so everyone who visits that day sees the same digits. A link can pin another grid: the address carries the size, the difficulty, and the seed. New game deals a fresh puzzle and writes that seed into the address, so the link you copy is the puzzle on the screen. Changing the size or the difficulty deals the same seed again at that setting.

On screen a 0 is drawn as a violet sun and a 1 as a teal moon; given cells sit on a tinted tile and cannot be changed. Tap an empty cell to place a sun, tap again for a moon, and a third time to clear it. Right-click, or press and hold on a phone, to go the other way. The arrow keys move the selection, 0 and 1 fill the selected cell, and Backspace clears it.

Three suns or three moons in a row, a line with too many of one symbol, and two identical lines are marked as soon as they appear. Undo and redo walk your moves. Hint fills one cell the rules already force and names the idea behind it. Check says the grid is unfinished, has a mistake, or is solved. Reset clears your cells and keeps the givens. Print uses the browser. Download PDF builds a black and white copy of the puzzle on the screen. Packs, with the answer key at the back, are on the printable Binairo page.

Beginner strategies

Pairs. Two equal digits side by side, 0 0, must be closed off at both ends: the cell before and the cell after are 1s. This is the first thing to scan for in every row and column.

Gaps. Two equal digits with one empty cell between them, 1 _ 1, force the middle: it must be the opposite digit, or the line would hold three 1s in a row.

Counting. A row of 8 holds four 0s and four 1s. Once a row has its four 0s, every empty cell left in it is a 1. Keep a running count of each line; on a 10×10 grid the halves are five each.

Counting ahead. When a line still needs exactly one more 0, try each empty cell as that 0 and look at what the rest of the line would become. If a choice would force three 1s together somewhere else in the line, that cell cannot be the 0, so it is a 1. Medium grids are built around this step.

Unique lines. When a row is two cells from finished and one way of filling those two cells would copy a row that is already complete, the other way is the answer. Columns work the same way. Hard grids usually need this rule, and sometimes a short chain: suppose a digit, follow the forced cells, and if the line breaks a rule, the opposite digit was right. Easy grids, including the daily 8×8, fall to pairs, gaps, and counting.