Hashi Puzzles
Join the numbered islands with bridges until each one has exactly its number of ends, nothing crosses, and the whole map is connected. Tap between two islands for one bridge, again for two. Sixty maps, all solvable without guessing.
Short for hashiwokakero, and printed in English collections as Bridges.
Related Practice
What Is A Hashi Puzzle?
Hashi gives you a scattering of numbered islands and asks you to join them with bridges. Bridges run straight, horizontally or vertically, between two islands — never diagonally, and never over the top of a third island. Each island must finish with exactly its number of bridge ends touching it, no two bridges may cross, at most two bridges join any one pair, and when you are done you must be able to walk from any island to any other. The full Japanese name, hashiwokakero, means roughly "build bridges".
The Islands That Solve Themselves
Every hashi opens the same way: find the islands whose number leaves them no choice. Since an island can take at most two bridges in each direction, one whose number is exactly twice its available directions is completely determined before you draw anything.
| Number | Where | Directions | What follows |
|---|---|---|---|
| 8 | anywhere | 4 | Two bridges every way — nothing else reaches eight |
| 6 | on an edge | 3 | Two bridges every way |
| 4 | in a corner | 2 | Two bridges both ways |
| 7 | anywhere | 4 | At least one bridge in every direction |
| 5 | on an edge | 3 | At least one bridge in every direction |
| 3 | in a corner | 2 | At least one bridge both ways |
The second group is the more useful one to learn. An island marked 7 cannot take two bridges everywhere, but it must take at least one in each direction — because if any direction had none, the other three could supply at most six. That single line of reasoning opens more hashi puzzles than any other.
Connectivity is a tool, not just a finishing condition. If a bridge would leave a group of islands with all their numbers satisfied among themselves while other islands sit outside, that bridge cannot be right — nothing could ever join the two halves afterwards. Ruling it out on those grounds is usually what breaks a stuck puzzle open, and the hint here will say so when it applies.
Thinking In Ranges Rather Than Answers
A hashi is solved by narrowing, not by placing. For each possible span, ask two questions: what is the fewest bridges it could still carry, and the most? An island needing six with three neighbours forces a minimum of two on all three straight away. Every bridge you fix changes the bounds on its neighbours, and every span you eliminate by crossing changes them again. The puzzle is finished when every range has narrowed to a single number.
Why The Maps Stop At Eighteen Islands
Maps with twenty or more islands are easy to draw and much harder to guarantee. Every map here has to be finishable by deduction alone, and past eighteen islands only about eight in ten randomly generated maps are — so finding a good one takes hundreds of attempts and the page would keep you waiting. At ten to eighteen islands every map is built and proved in well under a second, which is why that is where the range ends.
Hashi Puzzles Frequently Asked Questions
What is a hashi puzzle?
A bridge-building puzzle. Join numbered islands with straight horizontal or vertical bridges so each island ends up with exactly its number of bridge ends — nothing crossing, at most two per pair, and everything joined at the end.
What are the rules exactly?
Four. Each island takes exactly its number of bridge ends. Bridges run straight, never diagonally and never over another island. At most two join any pair. And the finished map must be fully connected.
What is hashi short for?
It is short for hashiwokakero, roughly "build bridges". English collections sometimes call it Bridges. Like several types here it was popularised by the Japanese publisher Nikoli.
Where do you start a hashi?
With islands that have no choice. An 8 needs two bridges in all four directions — eight is the most it could take. A 4 in a corner has only two directions, so it takes two each way. Any island whose number is twice its available directions is fully forced.
What about numbers one short of the maximum?
They are the next most useful. A 7 with four directions must take at least one bridge each way, because the other three could supply at most six. The same gives a 5 with three directions one each way.
Why does connectivity matter while solving?
Because it rules things out mid-solve. If a group of islands would be fully satisfied among themselves while others sit outside, nothing could ever join the halves — so the bridge creating that group is impossible. It often breaks a stuck puzzle open.
Can two bridges join the same pair?
Yes — up to two, drawn as a double line, counting two ends at each island. That cap is why 8 is the largest number possible: two bridges in each of four directions.
Does every puzzle here have one answer?
Yes, and none needs guessing. A solver restricted to ordinary reasoning must pin every possible bridge; because each step is forced, the answer is the only one. A separate enumerator confirms it independently.