How to Solve Hashi Puzzles: A Step-by-Step Guide

Hashi puzzles, also called Bridges or Hashiwokakero, look like a scatter of numbered circles, and the first time you see one it isn't obvious where to begin. The good news: every Hashi puzzle is solved by pure logic, never guessing, and the whole thing comes down to a few simple deductions you can learn in minutes. This step-by-step guide shows you how to solve a Hashi puzzle, from the rules to the key techniques (forced bridges, the no-isolation trick, elimination, and connectivity), with clear examples along the way.

The rules of Hashi in 30 seconds

A Hashi puzzle is a grid scattered with islands (numbered circles). Your job is to connect them with bridges (straight lines) so that:

• Bridges run only horizontally or vertically between two islands, never diagonally.
• There can be at most two bridges between any pair of islands.
• Bridges cannot cross other bridges or pass through an island.
• Each island's number equals the total bridges connected to it.
• When you're done, all islands form one connected group, you can travel from any island to any other.

That last rule, connectivity, is what makes Hashi more than just local arithmetic. If you want the formal version with diagrams, the Hashi rules page lays it out, and the interactive how-to-play tutorial walks you through your first board.

Step 1: Place the forced bridges

The fastest opening move is to find bridges that must exist, regardless of anything else. These happen when an island's number is so high relative to its neighbors that there's only one way to satisfy it.

• An island whose number equals twice its neighbor count must use double bridges to every neighbor. A 4 with exactly two neighbors needs two bridges to each (2 + 2 = 4). An 8 (the maximum) always has four neighbors with double bridges to all.
• An island whose number equals its neighbor count, with three or four neighbors, needs at least one bridge to each. A 3 with three neighbors connects once to all three.
• A 1 or 2 in a corner with a single neighbor is forced to spend all its bridges that way.

Sweep the whole board for these guaranteed connections first and draw them in. On our easy Hashi puzzles, forced bridges alone solve almost the entire grid.

Step 2: Use the no-isolation trick

Here's a small but powerful rule. Two islands of value 1 can never be joined to each other if that would seal them off from the rest of the puzzle, because a single bridge between two 1s creates a closed pair that can't connect to anything else. The same idea applies to two 2s with a double bridge: don't fully satisfy a little group in a way that isolates it.

This "don't trap yourself" thinking flows from the connectivity rule, and it eliminates bridges that look tempting but would split the network.

Step 3: Eliminate impossible bridges

When no bridge is outright forced, switch to elimination: rule out connections that can't work, which often leaves only one option.

Ask of each possible bridge: "If I place this, can every affected island still reach its number?" If placing a bridge to one neighbor would leave another neighbor short, that bridge is impossible, so drop it. Removing options this way frequently turns an undetermined island into a forced one. This is the main technique on medium Hashi and above.

Step 4: Apply the connectivity rule

The connectivity requirement is your tiebreaker on harder grids. Because every island must end up in one single network, any bridge that's the only possible link between two otherwise-separate clusters is required, even if local counting alone didn't force it.

So when you're stuck, zoom out and look at the shape of what you've built. If two groups of islands have only one possible bridge between them, that bridge has to be there, or the puzzle could never connect. This reasoning is what cracks hard and expert boards.

Step 5: Chain your deductions

On bigger puzzles, no single technique finishes the job. You chain them: a forced bridge enables an elimination, which forces another bridge, which connectivity confirms, and so on. Work in passes:

1. Place all forced bridges.
2. Apply the no-isolation rule.
3. Eliminate impossible bridges.
4. Use connectivity to force the remaining links.
5. Repeat until the grid is complete.

Each pass unlocks a little more. And remember the golden rule of Hashi: you never have to guess. Our puzzles are logic-only certified, so if a move feels like a coin flip, there's a deduction you haven't spotted yet, keep looking.

A quick worked example

Picture a 3 island in a corner with exactly two neighbors: a 2 to its right and a 1 below it.

• The corner 3 has only two neighbors, and the most bridges it can send is two each (four total), but it only needs three. So it must use double to one neighbor and single to the other.
• The 1 below can take only one bridge, so the 3 connects to it once. That leaves two bridges for the 3, all going right to the 2 (a double bridge).
• Now the 2 is satisfied entirely by that double bridge, and the 1 by its single. Three islands, solved by counting alone.

That cascade, satisfy the most-constrained island, then watch its neighbors resolve, is the heart of every Hashi solve.

Where to start

The best way to make this click is to play. Begin with our easy Hashi puzzles, where forced bridges carry you through, then move to medium for elimination and hard for connectivity logic. For more advanced patterns, see Hashi strategy, and if you're brand new to the puzzle, start with what is Hashi.

Frequently asked questions

How do you solve a Hashi puzzle?

Start by placing forced bridges, connections an island must make because its number is high relative to its neighbors. Then use the no-isolation rule, eliminate impossible bridges, and apply the connectivity requirement that all islands must form one network. Chain these deductions in passes until the grid is complete. No guessing is ever needed.

What are the rules of Hashi?

Connect the numbered islands with horizontal or vertical bridges so that each island has exactly its number of bridges. There can be at most two bridges between any pair of islands, bridges cannot cross, and all islands must end up connected in a single group.

Do you ever have to guess in Hashi?

No. A properly made Hashi puzzle has exactly one solution reachable by pure logic. Our puzzles are logic-only certified, so if you feel the urge to guess, there's a forced bridge, an elimination, or a connectivity deduction you haven't found yet.

What is the first move in a Hashi puzzle?

Look for forced bridges, islands whose number can only be satisfied one way. An island whose value equals twice its neighbor count needs double bridges to every neighbor, and islands in corners with few neighbors are often forced too. Place all of these first.