Here are three advanced techniques for resolving complex situations in Takuzu/Binaro.
Look at the masks above: When you identify them in your game, whether in a row or a column, due to the rule stated above, there must be a 0 and a 1 in the empty cells (because 0 0 and 1 1 are impossible). We don’t know the order, but this gives us quantitative information that may be useful.
Example: If row 1 is composed as follows (`11010 _ _ 1 _ _`) and you know that the mask area contains `01` or `10`, then positions 9 and 10 must be occupied by `00` because the number of 1s will have reached its quota (5).
Tip: When you encounter difficulties, scan all the rows and columns of your grid and locate all the masks present.
Identify lines that are unbalanced in terms of filling. Lots of 0s and few 1s, or vice versa. Play
1. The sub-mask technique (on rows & columns)
Principle: Based on the fundamental rule of Takuzu, which states that it is forbidden to have more than two consecutive identical digits, we will identify masks within the grid that will give us valuable information.
1 _ _ 0
0 _ _ 1
0 _ _ 1
Look at the masks above: When you identify them in your game, whether in a row or a column, due to the rule stated above, there must be a 0 and a 1 in the empty cells (because 0 0 and 1 1 are impossible). We don’t know the order, but this gives us quantitative information that may be useful.
Example: If row 1 is composed as follows (`11010 _ _ 1 _ _`) and you know that the mask area contains `01` or `10`, then positions 9 and 10 must be occupied by `00` because the number of 1s will have reached its quota (5).
2. Avoiding “forced triplets”
Principle: This technique is a subtle extension of the rule of 0 and 1. It consists of identifying the cells that, if filled in a certain way, would create an impossible configuration elsewhere.
Examples (10×10 grid):
Row 3:
Row 8:
There is 1 digit 1 left to place on row 3 and 3 digits 0.
If we place the 1 in position 10 → the 3 digits 0 occupy positions 6, 7, 8, which is impossible because we cannot have more than 2 identical digits in succession.
Consequence: the 1 is not in position 10 → 0 occupies position 10 Line 3:
The same reasoning applies to line 8.
Row 3:
1 1 0 0 1 _ _ _ 1 _Row 8:
1 0 0 1 1 0 _ _ 1 _There is 1 digit 1 left to place on row 3 and 3 digits 0.
If we place the 1 in position 10 → the 3 digits 0 occupy positions 6, 7, 8, which is impossible because we cannot have more than 2 identical digits in succession.
Consequence: the 1 is not in position 10 → 0 occupies position 10 Line 3:
1 1 0 0 1 _ _ _ 1 0The same reasoning applies to line 8.
Identify lines that are unbalanced in terms of filling. Lots of 0s and few 1s, or vice versa. Play