Hashi rules

What you see

A rectangular grid with numbered circles scattered across it. The circles are called islands. Each island has a number between 1 and 8. The empty cells between islands are where your bridges will go.

The name hashiwokakero means “build bridges” in Japanese. In English, most people just call it Hashi or Bridges. Nikoli, the publisher behind Sudoku, popularized it in puzzle magazines starting in the 1990s.

The three rules

1. Bridge count. Each island's number tells you exactly how many bridges must connect to it. An island labeled 3 needs three bridges total, spread across one or more neighbors.
2. No crossing. Bridges are straight lines, either horizontal or vertical. A horizontal bridge between two islands blocks any vertical bridge that would pass through the same space (and vice versa).
3. One connected group. When you finish, every island must be reachable from every other island by following bridges. No island or island cluster can be isolated.

Bridge placement details

Two islands are neighbors if they share the same row or the same column with no other island between them. You can place either one bridge (single) or two bridges (double) between any pair of neighbors. There's no option for three.

A double bridge counts as 2 toward each island's required count. So an island with value 4 and exactly two neighbors could have double bridges to both. Or one single and one double and a single to a third neighbor if it had three.

Bridges only run straight. No diagonals.

Solving techniques

1. Forced bridges

Start by scanning for islands whose bridges are fully determined. Common examples:

• Value 1, one neighbor: must connect to that one neighbor.
• Value 8: double bridges to all four neighbors. No other option.
• Value 4, two neighbors: double bridges to both.
• Value 3, two neighbors: at least one bridge to each (the third goes somewhere, and with only two choices it must be a double to one of them).

2. Elimination

When an island needs more bridges than it has remaining capacity minus the maximum its neighbors can absorb, minimums emerge. Suppose an island still needs 3 bridges and has two neighbors that can each accept up to 2. Total available is 4, remaining need is 3, so excess is 1. Each neighbor must receive at least 1 bridge (2 minus 1). Place those minimums.

3. Connectivity

This is hashi's unique constraint. If skipping a bridge would leave one or more islands permanently disconnected from the rest, that bridge is required. On large grids, look for “chokepoints” where a single bridge is the only link between two regions.

4. Crossing conflicts

Placing a horizontal bridge blocks every vertical bridge that would cross it. Sometimes you can prove a bridge must exist because the alternative would block a bridge that's required by another island. Think of it as indirect forcing.

Mistakes to avoid

Ignoring connectivity until the end. The most common beginner mistake. You satisfy every island number perfectly but end up with two disconnected groups. Check connectivity throughout the solve, not just at the end.

Forgetting about crossings. A bridge you placed early can block a bridge you need later. Before committing to a bridge, glance at what perpendicular paths it might block.

Placing bridges greedily. Just because you can add a bridge doesn't mean you should. Place bridges only when logic demands them, not because they “seem right.”

Frequently asked questions