How to Play Hashi

The Rules

Hashi (橋, Japanese for bridges) is also known as Hashiwokakero or Bridges. The puzzle is played on a grid of numbered islands. Your goal is simple to state but endlessly satisfying to achieve: connect every island using bridges so that the number on each island equals exactly the number of bridges attached to it, and all islands form a single connected network.

Four rules govern how bridges work:

• Bridges run horizontally or vertically — never diagonally.
• At most two bridges can connect any pair of islands.
• Bridges cannot cross each other or pass through another island.
• Every island must be reachable from every other island — one connected network.

Every puzzle has exactly one solution. You never need to guess — pure logic carries you all the way through.

Basic Technique: Forced Connections

The easiest place to start is any island that has only one reachable neighbor. That island has no choice — all of its bridges must go to that one neighbor. If the island shows a 1, place a single bridge. If it shows a 2, place a double bridge. Done.

Look for corner and edge islands first. Because they sit at the margin of the grid with fewer directions available, they often have just one or two neighbors and yield immediate deductions.

Similarly, an island with value 2 and only one neighbor must connect with a double bridge. These quick wins populate your grid early and open up further deductions elsewhere.

Basic Technique: Maximum Bridge Logic

When an island's value equals twice the number of its reachable neighbors, every single connection must be a double bridge — there is no slack anywhere. A 4-island with exactly two neighbors must place double bridges in both directions. A 6-island with three neighbors must double every connection.

A looser version of this logic also applies: if an island needs more bridges than its neighbors can provide at single-bridge connections, some connections must be doubles. A 3-island with two neighbors must place at least one double — you may not know which one yet, but you know at least one exists.

Basic Technique: Large Island Deductions

High-value islands — those showing 5, 6, 7, or 8 — are powerful anchors. Since each connection can carry at most 2 bridges, a value-7island needs at least four neighbors (since 3 neighbors × 2 = 6, which isn't enough). When you spot a large-value island, count its reachable neighbors and calculate the minimum bridges each connection must carry.

Intermediate Technique: Preventing Isolation

Remember the connectivity rule: all islands must form a single network. This constraint eliminates many otherwise tempting bridge placements.

Before placing a bridge, ask: would this bridge, if it were the last one added to these islands, cut the puzzle into two separate groups? If yes, that bridge cannot be the final connection — though it might still be valid as a partial connection if other bridges remain to be placed.

A cleaner version: if a small cluster of islands — say, two islands with low values — could become fully satisfied while connecting only to each other, placing those bridges would strand them. That move is illegal. Use this to rule out otherwise plausible placements.

Advanced Technique: Parity Logic

Parity — whether a number is odd or even — is a surprisingly powerful tool in Hashi. Here's the key insight: a double bridge contributes an even number (2) to both islands it connects. A single bridge contributes an odd number (1) to both.

This means: if an island has an odd value (1, 3, 5, 7), it must have an odd number of single-bridge connections. If it has an even value (2, 4, 6, 8), it must have an even number of single-bridge connections (including zero).

In practice: consider two neighboring odd-value islands with no other shared neighbors. The bridge between them must be a singlebridge — because a double bridge would add 2 to each island's count, and two odd numbers cannot be satisfied by only even contributions. This single insight resolves many otherwise ambiguous positions on hard puzzles.

Advanced Technique: Constraint Propagation

On hard puzzles, no single technique cracks the whole grid. The real skill is chaining deductions — letting each conclusion tighten the constraints on neighboring islands.

The process looks like this: you determine that island A must connect to island B with a double bridge. That uses up all of B's capacity in that direction. B now has fewer remaining bridges to distribute among its other neighbors — which might force one of those connections to be a specific value. That in turn constrains a third island, and so on.

A useful habit: after placing any bridge, immediately revisit every island touched by that bridge. Recalculate how many bridges it still needs and how many neighbors remain reachable. Often a single placement triggers two or three further deductions in a cascade.

When you feel stuck, look for the island with the fewest remaining possibilities — the one where the gap between its value and its maximum possible connections is smallest. That's where the next forced move is hiding.

Putting It All Together

A reliable solving order for any Hashi puzzle:

1. Scan for forced connections. Find every island with only one reachable neighbor and place all its bridges immediately.
2. Apply maximum bridge logic. Find islands where value equals twice the neighbor count. Double every connection.
3. Work large islands first. High-value islands constrain the most cells and yield the most information early.
4. Check isolation risk.Before completing an island, verify it won't disconnect from the network.
5. Apply parity. For odd-value islands, count how many single bridges are required and see if any connections are forced.
6. Propagate constraints. After each placement, rescan every affected island. Let the chain of deductions run as far as it will go before seeking the next starting point.

No puzzle on WebHashi requires guessing. If you feel stuck, take a breath, use the hint button to get a nudge, and trust that the logic is there — sometimes you just need a fresh angle.

Ready to put this into practice?