遊び方 · asobikata
How to play
Hashiwokakero (橋をかけろ, “build bridges!”) is a logic puzzle published by Nikoli. Connect all islands with bridges so that every island has exactly as many bridges as its number says.
Count the bridges
The number on an island is how many bridges end there.
One or two
Islands can be joined by a single wooden bridge or a double vermilion bridge, never more.
Straight, no crossings
Bridges run horizontally or vertically and must not cross other bridges or islands.
One archipelago
In the end every island has to be reachable from every other one.
A solved puzzle
Controls 操作
Click the water between two islands to build a bridge, again for a second one, a third click removes them.
Or drag from an island towards its neighbour, or click two islands one after the other.
Right click / Shift + click removes a bridge.
Ctrl Z Undo · Ctrl Y Redo · H Hint
Finished islands turn green, overfull ones red. Stuck? Ask the SAT solver for a hint or to check your bridges.
Under the hood 仕組み
Every possible bridge e between two neighbouring islands gets two boolean variables: e₁ (at least one bridge) and e₂ (a second bridge), with e₂ → e₁ so that every arrangement has exactly one model.
¬e₂ ∨ e₁An island with number n needs exactly n of its variables to be true, written as clauses over all combinations. Crossing bridges exclude each other:
¬h₁ ∨ ¬v₁Connectivity is hard to express in CNF, so it is added lazily: whenever the solver returns separate groups of islands, a clause demanding a bridge out of such a group is added and the solver runs again.
The generator grows a random archipelago and proves uniqueness by blocking the found solution and asking the solver for another one. Try the different solver modes in the lab.
よくある質問 · FAQ
Questions about Hashiwokakero
- What is Hashiwokakero?
- Hashiwokakero (橋をかけろ, “build bridges”), also called Bridges or Hashi, is a Japanese logic puzzle published by Nikoli. The grid shows numbered islands; you connect them with horizontal and vertical bridges so that every island has exactly as many bridges as its number, no bridges cross, and all islands form one connected group.
- How many bridges can connect two islands?
- At most two. A single bridge or a double bridge may join two islands that are in the same row or column with nothing in between.
- Can bridges cross each other?
- No. Bridges run straight horizontally or vertically and may neither cross other bridges nor pass over islands.
- Do all islands have to be connected?
- Yes. In a finished puzzle you can travel from any island to any other over the bridges, the islands form a single network.
- Is there always exactly one solution?
- On Hashi, yes: every generated puzzle is checked by a SAT solver, which proves that no second solution exists, so you never have to guess.