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Takuzu is a logic-based number placement puzzle. The objective is to fill a (usually 10×10) grid with 1s and 0s, where there is an equal number of 1s and 0s in each row and column and no more than two of either number adjacent to each other. Additionally, there can be no identical rows or columns. Takuzu is distributed in the French publications Le Figaro, Ludojeux. and 20 Minutes
Takuzu is also known as the Binairo.
- Each row and each column must contain an equal number of 0s and 1s. Therefore, if the required number of 0s or 1s is reached in a row or a column, the remaining cells must contain the other digit (1xx101 → 100101).
- More than two of the same digits can't be adjacent. Therefore, if two adjacent cells contain the same digit, the cells next to the digits must contain the other digit (xxx00x → xx1001). Likewise, if two cells contain the same digit with one empty cell in between, this empty cell must contain the other digit, because otherwise three same digit appears (x1x1xx → x101xx).
- Eliminate the impossible. For example, if the sixth cell in 110xxx is made a 1, balancing the number of 0s and 1s forces a trio to appear (110xxx → 110xx1 → 110001), so it can't be a 1. Therefore, the sixth cell must contain a 0 (110xxx → 110xx0).
- Each row and column is unique (100101 & 1001xx → 100101 & 100110).
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