Nikoli Logic Classic • Bridges
Bridges (Hashiwokakero)
Connect numbered islands with orthogonal bridges. No crossings, at most 2 bridges per strait, and unite the whole archipelago into a single network!
Loading Bridges archipelago...
Hashiwokakero (Bridges) Rules
Invented by Nikoli in 1990 under the name Hashiwokakero (“building bridges”), this game challenges your spatial planning and graph connectivity deduction skills:
1. Degree CluesThe number inside each circular island represents exactly how many bridges must attach to it.
2. Double Bridge MaximumBetween any two directly visible islands, you may place zero, one, or at most two bridges.
3. Orthogonal OnlyBridges must travel strictly horizontally or vertically. Diagonal bridges are never allowed.
4. Single Connected ArchipelagoEvery island must be reachable from every other island. Creating disconnected loops or isolated pairs is invalid.
Master Deductions & Theorems
- The Maximum Capacity Rule: Since each neighbor can receive at most 2 bridges, an island with 4 neighbors has a maximum capacity of 8. If an island requires 8 bridges, it must have double bridges to all 4 neighbors! Similarly, a 7-island must send at least 1 bridge to every available neighbor.
- Corner & Edge Caps: An island located in a corner can have at most 2 neighbors (max capacity 4). If a corner island requires 4 bridges, it must send double bridges to both neighbors immediately. A 3-island in a corner must send at least 1 bridge in both directions.
- Avoiding Early Isolation (The 1-1 Rule): Two 1-islands can never be connected directly to each other unless they are the only two islands in the puzzle. Connecting two 1-islands creates an isolated closed system of size 2, violating the single connected component requirement.
- Orthogonal Line-of-Sight: Bridges cannot leapfrog over intermediate islands. Always scan straight paths to see which islands can actually reach each other without being blocked.