How to Solve Hashi (Bridges): A Strategy Guide

Updated June 2026

Hashi — Bridges, or Hashiwokakero in full — gives you a scatter of numbered islands and asks you to join them with bridges. The numbers and a no-crossing rule do almost all the work once you learn to count an island's options. This guide covers the forced moves and the connectivity logic that finish a board cleanly.

The rules

• Bridges run straight. Each bridge connects two islands horizontally or vertically — never diagonally — in a straight line with no island in between.
• At most two between a pair. Any two islands may be joined by one or two bridges, no more.
• Bridges never cross. No bridge may pass over another bridge or through an island.
• The number is the total. Each island's number equals the total count of bridge-ends meeting it.
• One network. When finished, every island must be reachable from every other — the whole thing is a single connected group.

Count each island's capacity

Everything in Hashi starts with a simple count: how many bridge-ends can an island possibly support? It equals the number of neighbours it can reach in a straight line, times two (since each connection allows up to two bridges) — capped at two per direction. Compare that capacity to the island's number. When they are equal, the island is fully forced: every available direction takes the maximum it can. That single comparison places a surprising number of bridges before you do anything clever.

The classic forced numbers

Some numbers force themselves the moment you look at how many directions they have.

• An island showing the maximum for its position — a corner "4", an edge "6", or an interior "8" — must run double bridges in every available direction. These are the anchors you build out from.
• A high number with one cramped direction is nearly as good. A "7" in the middle with four neighbours needs seven of its possible eight ends, so at least three directions are doubles and the fourth is at least a single — usually enough to place several bridges at once.
• A lone "1" facing a single neighbour takes exactly one bridge there, and a "2" with one neighbour takes a double.

Don't isolate a sub-network too early

The connectivity rule is not just the finish line — it forbids moves along the way. Never complete a bridge that would seal off a small group of islands from the rest before every island is connected. The textbook case is two "1" islands sitting next to each other: joining them with a single bridge would satisfy both numbers but trap them as an island of two, cut off forever. So that bridge is illegal, which tells you each of those "1"s must instead connect outward. Watching for "this would close a loop early" resolves many spots that the numbers alone leave open.

Use the no-crossing rule as elimination

Every bridge you draw blocks the lane it occupies. If two islands could only have connected through a line that is now crossed by an existing bridge, that connection is dead — remove it from your mental options and recount the affected islands. Often a planned bridge crossing forces a different island to send its bridges elsewhere, which then becomes a forced move.

Re-count after every bridge

Hashi rewards bookkeeping. Each time you commit a bridge, reduce the remaining need on both islands it touches, and recompute their leftover capacity in the still-open directions. An island that needed 3 more ends across two open directions, after one direction gets capped at a single, now needs 2 more from one direction — forced to a double. This running subtraction is the engine; most "hard" boards are just long chains of it.

A reliable order of attack

1. Place all maximum islands (corner 4, edge 6, interior 8) as full doubles.
2. For every island, compare its number to its capacity and place any forced bridges.
3. Avoid any bridge that would isolate a sub-group before the whole board is linked.
4. After each bridge, recount both endpoints and re-check for new crossings that kill options.
5. Repeat until every number is met and all islands form one network.

A well-formed Hashi has a single solution you can reach by counting and connectivity alone, so guessing is never required — there is always an island whose remaining need is forced by the room it has left.