Strategy guides · Takuzu online
How to solve Takuzu (binary) puzzles: rules and strategies
Takuzu, also called a binary puzzle, asks you to fill a grid with two symbols. Frostfire uses fire and ice instead of 0 and 1, and adds links between cells. The rules are short, and a handful of patterns solve almost every board without guessing.
The rules
Fill every cell with fire or ice. No more than two of the same symbol may sit side by side in a row or column. Every row and column holds as many fires as ices. In Frostfire, two cells joined by = hold the same symbol, and two joined by × hold different ones.
1. Pairs push outward
Two identical symbols side by side can't become three, so the cells at both ends of the pair must hold the other symbol. Scan every row and column for pairs first; this alone fills a large part of an easy board.
2. Gaps get filled
A single empty cell between two matching symbols must hold the other symbol. A fire, a gap and a fire means the gap is ice.
3. Count to half
In a row of six, three cells are fire and three are ice. Once a row has its three fires, every empty cell left is ice. When a row is one short of half, check where the last one could go without making three in a row: often only one spot works.
4. Use the links
An = between two cells means you can treat them as one: if one is known, so is the other. An × between them means exactly one fire and one ice, which counts toward the row's half even before you know which is which.
Common mistakes
- Checking rows and forgetting columns. Every rule applies to both.
- Counting a × pair as unknown. It always contributes one of each.
- Guessing near the end. If you're stuck, recount every line against the half rule.