Puzzle guide
How to solve Takuzu
Takuzu is a grid of light and dark circles. It has just three rules, and each of them turns into a little trick you can spot at a glance. Learn the tricks below, and you can fill a whole board circle by circle.
The rules
- Put a light or a dark circle in every cell. None stays empty.
- Never three of the same side by side in a row or column.
- Every row and every column has as many light circles as dark ones.
- No two rows are the same, and no two columns are the same.
A solved puzzle
Your first moves
- Look for two of the same side by side. The cells at both ends get the other colour.
- Look for two of the same with a gap between them. The gap gets the other colour.
- Count every row and column. As soon as one colour reaches half, the rest is the other colour. The app shows how many of each a row or column still needs.
- When a row is almost full, compare it with the finished rows. It must not become a copy of one.
Techniques, step by step
Two side by side
Two light circles stand next to each other. A third light one beside them would make three in a row, which is not allowed. So the cells at both ends of the pair are dark. This is the move you will make most often, in rows and in columns alike.
Fill the gap
Two light circles with one empty cell between them. If the gap were light, there would be three light circles side by side. So the gap is dark. Pairs and gaps together already solve a large part of every easy board.
Count to half
A row of six cells has three light and three dark circles. This one already has three dark circles, so it has no room for another. Every empty cell in it is light. Counting works best near the end of a row, but it can also help early: a row of eight with four dark circles is done with dark.
No two rows alike
The top row has two empty cells left, and it needs one light and one dark circle. One of the two ways would make it exactly the same as the row below it, which is not allowed. So it must be the other way: the framed cell is light. This only matters when a row has two cells left and another finished row matches it everywhere else, but on bigger boards it often gives the last step.
Try every way for one row
When none of the tricks above helps, take one row or column and think through every way it could still be filled while keeping all three rules. If one cell has the same colour in every way that works, that colour is right. For example, in a row of six that needs two more dark circles, some ways would make three alike, and the ones that are left often all agree on a cell. Medium, hard and expert boards need this more and more often.
Common mistakes
- Only checking rows. Every rule is true for columns too. A move that is fine in its row can make three alike in its column.
- Losing count. Look at the small numbers beside each row and under each column: they show how many light and dark circles are still needed.
- Forgetting the last rule. Two rows or two columns may never be the same. It is the rule players forget most, and the one the hard boards rely on.
- Stopping when the warnings are gone. A board with no warnings can still have an empty cell. Every cell must be filled.
Questions and answers
Ready to play?
Pairs, gaps, counting to half and rows that must differ: four quick tricks, and the rest is patience. Pick a board and try them out.