Sudoku, kakuro, takuzu: what sets 123doku apart
Sudoku, kakuro, takuzu and 123doku look alike from a distance: a grid, cells to fill, a solution you reach without guessing. Up close they ask for different things. This page says what each one constrains, what it forbids, and where 123doku sits among them.
Sudoku: never repeat
You place the digits 1 to 9. The constraint is uniqueness: no digit repeats in a row, in a column, or in a nine cell region. Nothing is added up. You solve a sudoku by elimination, cell by cell, ruling out the digits already taken elsewhere.
Kakuro: a sum, with no digit twice
Kakuro brings in addition. Every run of cells, across or down, carries a total to reach, and the digits that make it up must all differ. Two constraints at once: the sum, and uniqueness inside each run.
Takuzu: two values, and a balance
Takuzu, also called binairo, knows only two values, 0 and 1. Each row and each column must hold as many of one as of the other, never three alike in a row, and no two rows may be identical. Again, no addition anywhere.
123doku: reach a total, without touching
123doku places stones weighing 1, 2 or 3. Each row and column shows the total it must reach. Weights repeat as often as needed: it is their sum that is constrained, not their uniqueness. The only ban is on contact: two stones of the same weight cannot touch side by side. Diagonally, they may.
The four, side by side
| Game | What you place | What is constrained | What is forbidden |
|---|---|---|---|
| Sudoku | the digits 1 to 9 | nothing to add up | repeating a digit in a row, a column or a region |
| Kakuro | the digits 1 to 9 | the sum of each run | repeating a digit inside the same run |
| Takuzu | 0 or 1 | the balance of each row and column | three alike in a row, two identical lines |
| 123doku | stones weighing 1, 2 or 3 | the total of each row and column | two stones of equal weight touching side by side |
What they share, and it is the heart of it
All four make a single promise: a well built grid has one solution, and that solution can be proved. You never take a chance. That is what separates a logic puzzle from a game of luck, and it is what 123doku borrows. It takes none of their rules; it takes their standard.
Which one to pick
None is better than the others. They simply ask for a different mental move.
- You like ruling out, hunting for what is already taken: sudoku.
- You like breaking a sum apart: kakuro.
- You like constraints of shape and rhythm: takuzu.
- You like tuning a total while never repeating two neighbours: 123doku.
None of the four needs any prior knowledge, and there is no mental arithmetic beyond adding small numbers.
