Connect islands in Hashi
Hashi asks you to satisfy each island’s bridge count while keeping every island in one connected network. Local totals and the whole-board connection must both work.
By Zehano · Original AI-assisted explanation and worked example · Updated 16 October 2026 · Editorial approach
A worked example
Imagine an island labelled 3 with only two visible neighbours: one to its right and one below. Because a pair of islands can have at most two bridges, neither direction can supply all three. Each direction therefore needs at least one bridge, and one of them needs a second. Now suppose the lower neighbour is labelled 1 and has no other connection. Its single bridge completes that neighbour, so the right-hand connection must contain two. This is a deduction from capacities, not a guess about which arrangement looks neat. After drawing those bridges, trace a route toward the other islands. Correct counts in this small group are not enough if the group becomes permanently isolated from the rest of the board.
Try it in three steps
- Count available directions before drawing. Only the nearest unobstructed island in the same row or column can be a neighbour; bridges cannot pass through another island or cross an existing bridge.
- Compare the remaining bridge requirement with the remaining capacity. Update both ends whenever you add or remove a bridge, because the same bridge contributes to two island totals.
- Finish with a connectivity check. Start at any island and follow bridges, keeping track of every island you can reach. A completed solution must reach them all.
What to watch for
Two islands labelled 1 can form a valid pair by themselves, but joining them is not a valid final choice on a larger board if it isolates them from all other islands. Check the complete network as well as individual numbers.
Apply it to your own material
Choose one topic from your current course or project. Write down the question you want to answer, make an attempt, and keep a note of how you checked it. Use the example above as a pattern; replace its subject matter and assumptions rather than copying an answer into a different task.
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