Binary Puzzle

How to play Binary Puzzle (Takuzu / Binairo)

Binary Puzzle — also known as Takuzu, Binairo or simply the 0/1 puzzle — is a logic puzzle played on a square grid that you fill entirely with two symbols: 0 and 1. It is often described as a mix of Sudoku and a crossword of numbers, but the rules are even simpler and every puzzle can be solved by pure reasoning, never by guessing. A handful of cells are given at the start; your job is to work out the rest so that three straightforward rules hold across the whole grid. Because each puzzle has exactly one solution, there is always a logical next step waiting to be found. This version offers three sizes — a gentle 6×6, a meatier 8×8 and a full 10×10 challenge — each timed and scored so you can chase a place on the leaderboard.

The goal

Fill every empty cell with a 0 or a 1 so that the finished grid obeys all three rules at once: no three identical symbols line up in a row or column, each row and each column contains an equal number of 0s and 1s, and no two rows are the same and no two columns are the same. When the whole grid is filled and all three rules hold, the puzzle is solved. The starting clues can never be changed — they are locked — and there is only ever one arrangement of 0s and 1s that satisfies everything.

The three rules

• No three in a row. You may never place three identical symbols next to each other, either horizontally or vertically. So 0 0 0 and 1 1 1 are forbidden as consecutive triples, but 0 0 1 or 1 0 0 are perfectly fine. Pairs are allowed; it is only the third neighbour that breaks the rule.
• Balance every line. Each row and each column must contain exactly the same number of 0s as 1s. On a 6×6 grid that means three of each per line; on 8×8 it is four of each; on 10×10 it is five of each. As soon as a line already holds its full quota of one symbol, every remaining empty cell in that line must be the other symbol.
• No repeated lines. When the grid is complete, no two rows may be identical and no two columns may be identical. Two lines that would end up as the exact same pattern of 0s and 1s are not allowed, so this rule often decides the final few cells.
• Every valid puzzle has one and only one solution. You never have to guess: if a cell cannot be logically determined, the puzzle would have more than one answer, which we never generate. Each grid we hand you is machine-checked to have a single unique solution before you ever see it.

Making moves

Tap any empty cell to cycle it through the values: blank becomes 0, another tap turns it into 1, and a third tap clears it back to blank. The two symbols are drawn in two clearly different colours — a cool blue disc for 0 and a warm amber disc for 1 — with the digit shown as well, so you can read the board at a glance and never mix them up. The clue cells you were given are drawn with a heavier, locked style and cannot be changed. As you play, any cell that breaks a rule right now — a third-in-a-row, a line with too many of one symbol, or a duplicated completed line — is ringed in red so you can spot and fix mistakes early. A running timer and a mistake counter sit above the board, and you can start a fresh puzzle or switch size at any time.

Solving techniques (no guessing needed)

• Avoid the triple. Whenever you see two identical symbols side by side, the cells on both ends of that pair must be the opposite symbol — otherwise you would make three in a row. This single idea, applied again and again, cracks open most of the board. Look for pairs like 1 1 and immediately place 0s at either end.
• Close the gap. A gap of one cell flanked by the same symbol on both sides — for example 0 _ 0 — must be filled with the opposite symbol, because filling it to match would create a forbidden triple. So 0 _ 0 becomes 0 1 0 and 1 _ 1 becomes 1 0 1 every time.
• Complete the count. Track how many 0s and 1s each row and column already has. Once a line contains all of its allowed 0s (three on 6×6, four on 8×8, five on 10×10), every remaining blank in that line must be a 1, and vice versa. This often finishes whole rows or columns in one sweep.
• Use uniqueness. Near the end, compare almost-finished lines. If filling a line one way would make it a copy of another completed line, it must be filled the other way. Combining the no-repeat rule with the balance count frequently pins down the last stubborn cells without any guesswork.

Winning and scoring

You win the moment every cell is filled and all three rules hold across the entire grid — the app checks continuously and shows a win banner as soon as the last correct symbol lands. Your score rewards speed and accuracy: it starts at a base of 8000 and subtracts one point for every second you take plus 250 points for every mistake, never dropping below 1. In formula terms the score is max(1, 8000 − seconds − mistakes × 250), and it is capped so it always fits the leaderboard. A mistake is counted each time you place a symbol that disagrees with the puzzle’s unique solution, so careful, deliberate play beats frantic tapping. Sign in to save your best score per size to the online leaderboard; otherwise your best result is kept on your device.

Strategy tips

• Start with the pairs. Scan the whole grid for existing pairs of identical symbols and the single-cell gaps between matching symbols; these force their neighbours immediately and give you a strong foothold before you have to think harder.
• Keep a running tally. Glance along each row and column and count how many of each symbol are already placed. Lines that are one short of their quota are the easiest place to make a certain move without risk.
• Save the uniqueness rule for last. The no-repeated-lines rule is most powerful when most cells are filled, so lean on the triple and balance rules first, then use uniqueness to settle any remaining ambiguity at the finish.

Frequently asked questions