Hashi vs Sudoku: How the Two Puzzles Compare
Niels Glodny ·
Hashi and Sudoku have a lot in common. Both are pure logic with no arithmetic beyond counting, both have exactly one solution, and both owe their names to the same Japanese publisher, Nikoli. The difference is in what you do: Sudoku fills digits into a fixed 9×9 grid, while Hashi draws lines between clues on a board of any size.
Side by side
| Sudoku | Hashi | |
|---|---|---|
| What you do | Write a digit from 1 to 9 in every empty cell | Draw bridges between numbered islands |
| Board | Always 9×9 | Any size; 3×3 to 60×60 in this game |
| Rules | Each row, column and 3×3 box holds every digit once | Each island gets as many bridges as its number, at most two per pair, no crossings, one connected network |
| What a rule covers | One row, column or box | Connectivity covers the whole board |
| First published | 1979 in Dell Magazines (US) as Number Place; named Sudoku by Nikoli in 1984 | 1990 in Puzzle Communication Nikoli, issue 31 |
| Complexity | NP-complete for the general n²×n² grid | NP-complete |
How the solving differs
Sudoku hides its state, Hashi shows it. In Sudoku, the hard part is keeping track of which digits are still possible in each cell. Serious solvers write these candidates into the corners of cells. In Hashi, what is still possible is mostly visible on the board: you can see each island’s neighbours and the bridges already drawn. You count rather than remember.
Hashi has a rule that reaches across the board. Every Sudoku rule is about one row, column or box. Hashi’s rule that all islands must connect is about the whole board at once. A bridge can be wrong because of what it does to a group of islands on the other side. Nothing in Sudoku works like that, and it is where most Hashi mistakes come from.
The first techniques are similar. A Sudoku cell with only one possible digit is filled at once. A Hashi island whose neighbours can take exactly as many bridges as its number is also settled at once. Both puzzles start with these “only one way” moves, and in both, the harder puzzles end with following an assumption until it breaks.
Board size changes Hashi more than Sudoku. Every Sudoku has 81 cells, and difficulty comes from how few clues there are and how they interact. The fewest clues a Sudoku with one solution can have is 17. Hashi boards grow, and a 35×35 board has around two hundred islands. Difficulty there is as much about endurance and not missing anything as about any single deduction.
If you like Sudoku
The first Hashi moves will feel familiar: look for the place with only one option, fill it, look again. What takes getting used to is the connectivity rule. Start with the rules and the beginner techniques; the campaign starts at 3×3, so the first puzzles take under a minute.
Puzzles closer to Hashi
If what you like about Hashi is drawing lines and keeping a network together, these are nearer relatives than Sudoku:
- Slitherlink. Draw a single loop along the grid lines. A number in a cell says how many of its four sides the loop uses.
- Masyu. Draw a single loop through the centres of cells that passes every circle. It must turn on black circles and go straight through white ones, with extra rules for the cells next to them.
- Numberlink. Join each pair of equal numbers with a path. Paths may not cross or share a cell.
Kakuro, often listed with these, is closer to Sudoku: you fill cells with digits that add up to the clues.
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