Guide to binary puzzle rules

Binary Puzzle Rules: Balance, Triples, and Links

A clear guide to binary puzzle rules, including balanced rows and columns, forbidden triples, and same-or-different connector clues.

Paws & Pairs cat and dog binary logic puzzle grid on Android

Binary puzzles turn two simple symbols into a surprisingly deep deduction system. You may see zeroes and ones, suns and moons, colors, or—in Paws & Pairs—cats and dogs.

Different versions sometimes add a rule that completed rows and columns must be unique. Paws & Pairs focuses on balance, no triples, and explicit link clues, so use the rules shown by the puzzle you are actually playing.

01

Rule 1: balance each line

Every row and every column contains the same number of each symbol. A 6×6 grid therefore needs three cats and three dogs per line.

Counting is most useful when a line is close to its limit. Once all cats have been placed in a row, every open cell in that row must be a dog, and the same logic applies to columns.

02

Rule 2: never make a triple

Three identical symbols cannot appear consecutively from left to right or top to bottom. Diagonals do not count unless a particular game explicitly says otherwise.

Patterns such as cat–cat–blank and blank–dog–dog force the blank to be the opposite animal. A cat–blank–cat pattern also forces a dog into the middle.

03

Rule 3: satisfy link clues

Paws & Pairs uses a double line between neighboring cells to mean same and an × to mean different. The clue applies only to the two cells it connects.

Treat a link as a relationship rather than a free placement. Once one cell is known, the linked cell follows; before that, surrounding balance and triple rules can determine which orientation works.

04

Know which rules your app uses

Classic Takuzu often requires every complete row and column to be unique. Tango-style variants frequently replace or supplement that rule with connectors.

Paws & Pairs teaches its active rules in the interface and explains them through hints. That makes it safer to follow the board in front of you than to assume every binary puzzle uses an identical rulebook.

Paws & Pairs app icon

Put the guide into practice

Try it in Paws & Pairs

Paws & Pairs is a relaxing Takuzu-style logic puzzle for iOS and Android. Balance cats and dogs, avoid three matching animals in a row, follow same-or-different links, and solve every grid by deduction—never guessing.

Get it on Google Play

Common questions

FAQ

Do diagonal triples count?+

No. The standard no-triples rule applies horizontally and vertically, not diagonally.

Must every row be different?+

That is a common classic Takuzu rule, but not every connector-based variant uses it. Follow the rules stated by your puzzle.