How to Solve Bridges (Hashi) Puzzles
A Bridges puzzle starts as a scatter of numbered islands floating on a grid, and your job is to wire them together into one connected web. Each island wears a number that says exactly how many bridges must touch it, you may run at most two bridges between any pair, and no bridge is ever allowed to cross another. It sounds open-ended, but it is really a pure-logic puzzle: in a good board, every bridge is forced by the numbers if you read them in the right order. This guide walks you from the bare rules to the handful of moves that quietly solve almost any layout - starting with the islands that have no freedom at all and chaining outward from there.
What a Bridges puzzle actually is
Bridges - also called Hashiwokakero, or just Hashi - gives you a grid dotted with circular islands, each holding a number from 1 to 8. That number is the count of bridges that must connect to that island, no more and no fewer. You draw the bridges as straight lines, only horizontally or vertically, joining one island directly to another.
Three rules shape everything else. A bridge runs in a straight line between two islands with nothing in between. You may place one bridge or two between the same pair, but never three. Bridges may not cross each other, and they may not pass straight through an island to reach one beyond it. When you are finished, every island shows exactly its number, and - this is the rule people forget - the whole set of islands must form a single connected network, so you could travel from any island to any other by walking across bridges.
Read the board before you draw anything
The fastest solvers do almost no guessing because they spend the first minute just looking. Pick an island and ask a single question: how many directions can it actually send a bridge? An island only ever connects to its nearest island in each of the four compass directions - up, down, left, right - so the most neighbours it can possibly have is four, and each neighbour can take at most two bridges. That gives every island a ceiling of eight, and a much lower ceiling once you notice walls and corners cutting off directions.
The whole game turns on comparing an island's number to that ceiling. When the number equals the maximum the island could possibly send, there is no choice left: every available connection must be filled, often with two bridges. Those are the islands you draw first, because they hand you free, certain bridges that the rest of the puzzle grows from.
Count the exits first. Before placing a single line in Mochi Bridge, glance at each island and silently count its possible directions. The ones whose number matches that count are your opening moves - they cost you nothing to find and unlock everything after.
The islands that force all their bridges
Some islands have only one legal arrangement, so you can fill them on sight. These are the seeds of the whole solution, and three patterns cover most of them.
- A corner 2. A corner island can only reach two directions, and a 2 there needs two bridges total. With two directions sharing two bridges, you draw a single bridge in each direction - both connections are guaranteed.
- An edge 3. An island against an edge has only three directions open. A 3 spread across three directions means one bridge in each, so all three single bridges are forced immediately.
- A centre number that maxes its neighbours. Anywhere on the board, when the number equals twice the count of available directions, every one of those directions must carry the full two bridges. A 6 with exactly three reachable neighbours, a 4 in a corner, an 8 in the open middle - each forces a double bridge to every neighbour at once.
The trick uniting them is always the same: number versus exits. A corner 4 fills both directions with doubles; an edge 6 fills all three with doubles; an open island showing 8 fills all four with doubles. Sweep the board for these before anything subtler, draw them in, and you have already finished a surprising slice of the puzzle.
Never isolate a sub-group
This is the rule that separates a Bridges board from a simple counting exercise, and the one beginners trip over last. Because every island must end up in one connected network, you are not allowed to make a move that seals off a little cluster from the rest of the board, even if every number in that cluster would be perfectly satisfied.
The classic trap is two islands each showing 1, sitting next to each other. A single bridge between them satisfies both numbers - but it also creates a closed pair that can never connect to anything else, because both islands are already full. Unless those two islands are the entire puzzle, that bridge is illegal. The same logic applies to any group: a 2 and a 2 facing each other, joined by a double bridge, are a sealed island of their own. Before you commit a bridge that finishes off two islands, check whether it strands them from everyone else.
Picture the whole map. Whenever a move would top out two islands at once, pause and trace whether the rest of the board can still reach them. In Mochi Bridge a finished but disconnected cluster is a dead giveaway you took a forbidden shortcut - back it out and look for the route that keeps everything joined.
Use "at least one" and "not zero" deductions
Not every helpful move is a full island. Often you can prove that a particular bridge must exist, or must carry at least one line, without solving its island outright. These partial certainties are the glue between your forced openings.
Suppose an island shows 3 and has only two neighbours. Three bridges across two connections means at least one of those connections carries two bridges - and more usefully, neither connection can be empty, because dropping either one leaves the other capable of only two. So both directions get at least one bridge straight away, even though you do not yet know which one doubles up. The same reasoning rescues a 4 with two neighbours: it must be a double on each side, fully forced. Whenever a number is large relative to its neighbour count, you can usually draw a first bridge to each neighbour even before the island is finished.
Chain the forced bridges
Solving Bridges is a chain reaction, not a one-shot calculation. Every bridge you commit changes the count of bridges an island still needs, which can turn a previously flexible island into a forced one. The rhythm is to place a certain bridge, update the running total on both islands it touches, then look again at those islands and their neighbours for the next thing that just became certain.
- Place the obvious openers. Fill every corner, edge, and maxed-out island whose number equals its capacity.
- Subtract as you go. Each time a bridge lands, lower the remaining count on both islands and note how many directions they have left.
- Re-check the neighbours. An island that needed 3 across three directions becomes a forced "fill the rest" the moment one direction gets capped.
- Cross off blocked lanes. When a bridge would now have to cross an existing one, mark that lane impossible - removing options is as powerful as adding bridges.
- Loop the connection check. Before finishing, confirm a single network and that no island sits stranded; if one does, an earlier "forced" move was actually a sealed group.
Most boards that feel stuck are not stuck at all - you have simply stopped updating. Re-walk the islands you thought were idle, subtract the bridges you have already drawn, and a fresh forced move almost always appears.
Common beginner mistakes
- Forgetting the single-network rule. Matching every number is necessary but not sufficient - if the islands split into two separate webs, the puzzle is unsolved.
- Drawing a third bridge. The cap between any pair is two. If an island still needs more, the extra bridges must go to a different neighbour.
- Letting bridges cross. Two lines can never intersect, and a bridge can never pass through an island. A planned route that crosses something is simply off the table.
- Sealing a 1-1 or 2-2 pair early. Joining two small islands that complete each other can lock them away from the network. Check connectivity before you commit.
- Guessing instead of counting. A well-built Bridges board never needs a coin flip. If you feel cornered, you have missed a forced bridge or a blocked lane somewhere behind you.
Where to go next
The quickest way to make these moves automatic is to play small, gentle boards until the corner, edge, and connection checks feel like reflexes. Mochi Bridge eases you in with hand-tuned layouts across its Berry, Citrus, Mint, Ocean, and Galaxy worlds, then opens an endless supply once you want a steady stream - and because there is no timer, you are free to read the whole board before drawing. If you enjoy the calm "what is already forced?" feeling of Hashi, the pure-logic puzzles below scratch exactly the same itch.