Hashi (Bridges) Guide: How to Solve Island Bridge Puzzles

1. The number on an island is a bridge budget

Each island number is a degree: the exact total of bridges touching it, counting a double bridge as two. The puzzle ends when every total matches, every island sits in one connected network, and no bridge crosses another.

Values here run from small endpoints up to a cap of 6 at the busiest junctions. A 1 is a leaf sending exactly one bridge; a 6 is a hub spending bridges in nearly every direction.

• Two islands can share at most two bridges; a pair never needs a third line.

2. Only direct neighbours can shake hands

A bridge runs straight along a row or column and stops at the first island it meets. You can only link an island to the one directly next to it, never to one further away with another island in between, because a bridge cannot hop.

Click one island, then another; each click on a legal pair cycles the link from none to single to double and back, so you assemble and dismantle with the same action.

3. Squeeze the small islands first

Start where constraints bite hardest: the smallest numbers with the fewest partners. A 1 that has one connectable neighbour is forced, and a 2 in the same lonely spot must send a double bridge.

Keep a ledger as bridges land: subtract each bridge from both islands and close any pair that would overshoot. Once an island reaches its number it accepts nothing further.

• A value of 3 with exactly two open partners must be one double and one single bridge, never three on one side.

4. Let leftover capacity force doubles

Most boards crack with a simple ceiling count: with m open partners, an island can still gain at most 2 times m bridges.

Compare that with what the island still needs. Needing more than 2 times (m minus 1) forces every partner to take at least one bridge; needing exactly 2 times m doubles them all; needing exactly m gives each a single.

• A 6 island with three neighbours must be three doubles, with no slack at all.
• A 5 island with three neighbours must be 2 + 2 + 1, sparing only one single bridge.

5. Never let a cluster cut itself off

The finished network is one connected piece, and that rule creates local duties: split the islands into two groups and at least one bridge must cross the gap, or the halves could never connect.

Use the check in reverse. If you satisfy a small group's numbers with internal bridges while it still has no link to the rest of the board, it is a dead end that can never be repaired. Undo and route one bridge outward before closing the group.

• A value-1 island is a door: make sure its single bridge points toward the network rather than sealing a pocket off.

6. Respect the corridors you draw

Crossings are forbidden, so every bridge claims a straight corridor. Before connecting a far pair, check that no existing bridge already threads across the ribbon it occupies.

Collision awareness cuts both ways: when two potential bridges would collide, one link is impossible, so an island may have fewer real partners than it appears to have.

• A bridge never passes through an island, so a line of three islands forces the middle one to make its own choices.

7. A reliable solving rhythm

List the forced singles and doubles first, then let satisfied islands shrink their neighbours' options. Medium is 7×7 with nine islands and Hard 9×9 with twelve.

The board flags slips the moment they happen: an island turns red when its bridges outnumber its value, and crossings are drawn red. Use Undo to step back one bridge and never borrow from one island to excuse another.

• Easy 5×5 boards with six islands are the place to rehearse the capacity count before graduating to denser water.