Paritu rules and solving techniques
Paritu is a binary logic puzzle: every cell gets a 0 or a 1. The name comes from parity: when you are done, every row and every column holds as many zeros as ones.
It is solved by deduction and never by guessing - every cell follows by force from the cells already placed. On striduel there are new tasks every day, free in the browser and playable without an account.
The rules
Some cells are given and cannot be changed; they are set apart in colour. You fill the empty ones yourself, and a tap cycles through: empty → 0 → 1 → empty.
- As many of each. Every row and every column ends up with as many zeros as ones. On a 4×4 grid that is two and two, on 6×6 three and three.
- Never three the same in a row. Neither across nor down may three identical digits follow one another. Two side by side are fine, three are not.
- On 6×6 only: no repeats. No two rows and no two columns are alike. On 4×4 this rule does not apply - there are too few possibilities for it to contribute anything.
Every task has exactly one solution, and it is always reachable without guessing. If you are stuck, there is a rule you have not applied yet - you have not been unlucky.
Strategy: three inferences that always hold
From a position the next move either follows by force or it does not - and then it is somewhere else that you keep looking. These three inferences carry the first two tiers almost on their own.
- Pair rule. Two ones sit side by side in a row. The cells directly to their left and right are therefore zeros by force: a one there would put three identical digits in a line, which the second rule forbids. Downwards the same inference holds.
- Gap rule. A zero, one empty cell, another zero. A one belongs in that gap by force - a zero there would make three zeros in a row.
- Line count. A 6×6 grid holds three zeros and three ones per row. Once a row holds three ones, every remaining cell in it is a zero by force - and you never have to look at a neighbouring cell to see it.
If you are stuck anyway, one of these has not been applied yet. There is no bad luck here: every task can be solved without guessing.
An example, step by step
A real 4×4 grid on the easy tier, solved with the same rules that apply in the game. Each step names the technique, the reason, and the cell that follows from it.
Step 1Pair rule - In column 1, row 2 and row 3 hold two ones one above the other. The cells directly before and after must therefore carry the other digit - otherwise three the same would stand one above the other. That settles: row 1, column 1 = 0; row 4, column 1 = 0.
Step 2Pair rule - In column 2, row 1 and row 2 hold two zeros one above the other. The cells directly before and after must therefore carry the other digit - otherwise three the same would stand one above the other. That settles: row 3, column 2 = 1.
Step 3Pair rule - In row 3, column 1 and column 2 hold two ones side by side. The cells directly before and after must therefore carry the other digit - otherwise three the same would stand side by side. That settles: row 3, column 3 = 0.
Step 4Gap rule - In row 4 two zeros sit with exactly one gap between them. The other digit belongs in that gap, or a run of three would appear. That settles: row 4, column 2 = 1.
Step 5Line count - row 1 already holds 2 zeros - half of its 4 cells. Every remaining cell in that line is therefore the other digit. That settles: row 1, column 4 = 1.
Step 6Line count - row 2 already holds 2 ones - half of its 4 cells. Every remaining cell in that line is therefore the other digit. That settles: row 2, column 4 = 0.
The techniques by name
These are the same names the game uses when it names a technique - in Deduction Rush it stands there after every answer. Read them here, play there, and you meet the same word again.
- Pair rule. Where two identical digits sit side by side, the cells to their left and right must carry the other one - otherwise three the same would stand in a line.
- Gap rule. Where a single gap sits between two identical digits, the other digit belongs in it.
- Line count. Once a row or column holds half of one digit, every remaining cell in it is the other.
- Unique lines. On 6×6 only: a filling that would repeat a row or column already complete drops out.
- Trial. On the hard tier it happens that you place a value on trial: if it leads to a rule violation, the other one is right.
Practise it yourself
In practice mode you can play Paritu on its own, as often as you like and on the tier you choose. None of it counts towards a leaderboard - it is the place to try things out.