Bridges Puzzle Strategy: Count Links and Keep One Network

Check the number and the network

A sound Bridges puzzle strategy asks two questions: does each island have the required number of bridge ends, and can you travel from any island to every other? Satisfying the first condition can still leave separate groups. Keep the connection question visible while you count, rather than postponing it until every number looks finished.

Nikoli's Hashiwokakero rules allow at most two bridges between a pair of islands and require one continuous network. Bridges cannot cross another bridge or pass through an island. The standard horizontal-and-vertical rules also appear in Simon Tatham's manual. Its optional no-loops variant is separate; ProjectGAMR's version permits cycles.

Use the available directions as a capacity limit

On this site's 3×3 starter, a corner island has two neighboring routes, a side island has three and the center has four. Each route holds zero, one or two bridges. A corner numbered 4 therefore needs a double bridge in both directions. A corner numbered 3 needs both routes, with one doubled.

These are local deductions about capacity. A corner numbered 2 can use two singles or one double, so its number alone does not determine the arrangement. Before filling its last available route, ask whether the resulting group would still have a way to reach the other islands.

Set up an original nine-island example

Label the island positions A B C across the top, D E F across the middle and G H I across the bottom. These letters are positional references for this exercise, not labels printed by the game. Use targets 2 3 2 / 3 4 3 / 2 3 2, with each slash starting another row.

A valid construction puts one bridge on every neighboring horizontal and vertical route. That uses six horizontal and six vertical singles. Each corner receives two ends, each side island three and the center four. Following these links reaches all nine islands. This demonstrates one solution; it does not claim the example has a unique answer.

Correct totals can hide two separate groups

Now replace that construction with singles on AB, AD, FI and HI, plus doubles on BE, DE, CF and GH. Leave every other route empty. Check the numbers: A has two; B and D each have three; E has four. C, F, G, H and I also meet their targets.

Nevertheless, A, B, D and E form a closed group. The remaining five islands form another. No bridge joins those groups, so the arrangement fails the puzzle's connection rule. A double supplies two ends at each endpoint, but it does not connect two different destinations. Counting bridge units and counting reachable islands answer different questions.

Rebalance four routes to reconnect the board

Repair the disconnected example by adding one bridge on BC and one on EF, then reducing BE and CF from doubles to singles. B, C, E and F each gain one end and lose one, so all island totals remain correct. The new links join the formerly separate groups into a network containing all nine islands.

That repair illustrates why adding a connection may require moving bridge capacity elsewhere. Simply drawing BC into the old arrangement would exceed B's and C's targets. Track the consequences at both endpoints of every change. A completed-looking region may need revision when its capacity prevents the whole board from connecting.

Apply the checks in the actual interface

ProjectGAMR's Bridges version checked on October 30, 2026 uses nine islands and controls between immediate neighbors. Tap a control to cycle through zero, one and two bridges, then back to zero. Changing a double to a single takes two taps through the empty state. The geometry offers no diagonal or crossing route.

Choose Check bridges after reviewing both conditions. New game generates fresh targets and clears the links; your board may differ from the exercise. Trace a route from one corner through the entire network, then recount changed islands. A cycle is allowed, but a separate completed component is not enough to finish.

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