Connect islands with bridges according to numerical clues. Create a single connected network without crossing bridges.
Rules: 1 Bridges must be straight lines connecting two islands horizontally or vertically. 2 Bridges cannot cross islands or other bridges. 3 Each island must have exactly as many bridges connected to it as its number indicates. 4 There can be at most two bridges between any two islands. 5 All islands must be connected into a single group.
Hashi (also known as Bridges or Chopsticks) is a logic puzzle published by Nikoli. The puzzle is played on a rectangular grid with islands (circles containing numbers). The goal is to connect all islands according to the rules.
Mathematical Significance: Hashi puzzles are based on graph theory concepts. Each island is a vertex, and bridges are edges. The puzzle requires creating a connected graph where each vertex has a specified degree (number of edges). The solution is unique for well-formed puzzles.
| Strategy | Description | Example |
|---|---|---|
| Island with "8" | An island with number 8 must have double bridges in all four directions (if possible). | An 8 in the middle requires 4 double bridges. |
| Island with "1" | An island with number 1 can only have one bridge, so mark other directions as impossible. | A 1 in a corner has only one possible direction. |
| Island with "2" at edge | An island with 2 on the edge of the grid must have both bridges in the same direction (double bridge). | A 2 on the left edge requires a double bridge to the right. |
| Forced connections | When an island needs more bridges than available directions, some directions must have double bridges. | A 5 with three available directions needs at least one double bridge. |
| Avoiding isolation | Ensure all islands remain connected to the main group. | Don't create separate disconnected groups of islands. |
| Difficulty | Solved | Best Time |
|---|---|---|
| Easy (6x6) | 0 | - |
| Medium (8x8) | 0 | - |
| Hard (10x10) | 0 | - |
| Expert (12x12) | 0 | - |
| Total | 0 | - |