How to play Hashi
Hashi is bookkeeping disguised as an archipelago: every island announces its bridge count, and simple arithmetic pins the network down. Here are the rules and the moves.
The rules
- Each numbered circle is an island; the number is exactly how many bridges must touch it (1–8).
- Bridges run horizontally or vertically between two islands with a clear line of sight.
- At most two bridges between the same pair.
- Bridges never cross other bridges or pass through islands.
- The finished network must be one connected whole — every island reachable from every other.
Controls
- Tap the gap between two aligned islands: once for a single bridge, again for a double, a third time to remove.
- Islands turn amber when their number is exactly met; over-full islands outline in red if you pause.
- Crossing attempts are rejected — the bridge simply won't place.
Solving strategies
- Capacity check. Count what an island's neighbors can still accept (at most 2 each). If that total equals the island's number, every link maxes out. A corner "4" with two neighbors: two doubles, done.
- The all-but-one rule. If skipping one neighbor leaves capacity below the island's number, at least one bridge to that neighbor is forced. This is the workhorse deduction — apply it everywhere.
- Ones and twos are picky. Two "1" islands may not be joined to each other if that would seal them off from the rest; a "2" pair likewise can't take a double. Use connectivity to prune options.
- New bridges cut sight lines. Every bridge you place blocks crossings — recount the neighbors of nearby islands after each placement; forced moves cascade.
- Finish with connectivity. If the numbers all match but two groups stand apart, a link is misplaced — the real solution is always one network.
A worked example
An edge island shows "5" with two visible neighbors — one across, one below. Maximum capacity is 2 + 2 = 4 from doubles... too little unless both are doubles plus — wait, 5 > 4 is impossible, so one of its neighbors must actually be reachable the other way: check the sight lines again after nearby bridges land. Say it truly has three neighbors with capacities 2, 2 and 1. Skipping the "1" leaves 4 < 5, so one bridge to the "1" is forced; skipping either "2" leaves 3 < 5, so a bridge to each "2" is forced as well. Four of five bridges placed by arithmetic alone — and the fifth follows as neighbors fill up.
Common mistakes
- Sealing off a pocket. Matching numbers isn't enough — a private two-island loop breaks the connectivity rule even if the counts are perfect.
- Forgetting bridges block sight. A bridge across a corridor removes island pairs that used to see each other — recount after every placement.
- Treating numbers as minimums. They're exact. An island with too many bridges is just as wrong as too few.
- Ignoring the doubles limit. Two is the max per pair — a "8" island needs all four directions doubled, no shortcuts.
Frequently asked questions
- What does "Hashi" mean?
- It's short for Hashiwokakero, Japanese for "build bridges" — the puzzle first appeared in Japanese puzzle magazines.
- Do I ever need to guess?
- No — every board here is generated so counting logic alone completes it, with exactly one solution.
- Is there a daily puzzle?
- Yes — a shared Daily Challenge with streaks, plus unlimited boards in three sizes. Free, no login.