Bridges

How to play Bridges (Hashiwokakero)

Bridges — known in Japan as Hashiwokakero, and often shortened to Hashi — is a pure logic puzzle in which you link a scattering of numbered “islands” with straight bridges. Every island shows a number, and that number tells you exactly how many bridge-ends must touch it. You draw only horizontal and vertical bridges, at most two between any pair of islands, and no bridge may ever cross another or pass over an island. When every island holds precisely its number of bridges and the whole group is joined into a single connected network, the puzzle is solved. There is no luck and no hidden information: every puzzle here is generated with exactly one solution, so a careful chain of deductions always gets you home. Play three sizes, race the clock, and post your score to the leaderboard.

The goal

Connect all the islands into one single network of bridges. Each island must end up with exactly as many bridge-ends as the number printed on it — count both ends of every bridge that touches it. When all the numbers are satisfied at the same time and you can travel from any island to any other by following bridges, you win. If even one island is short, over-filled, or cut off from the rest, the puzzle is not yet finished.

The board

The board is a rectangular grid dotted with circular islands, each carrying a number from 1 to 8. Easy boards use a small 5×5 grid with a handful of islands; Medium and Hard boards grow larger and add more islands, so there is more to keep track of. The empty grid cells are simply the water and the space through which your bridges run. Bridges are drawn as single or double straight lines between two islands that share the same row or the same column.

The four rules

• Exact count. Each island must be touched by exactly its number of bridge-ends. A “3” needs three bridge-ends in total — for example a double bridge on one side and a single bridge on another. A double bridge counts as two ends at each island it joins.
• At most two. Between any one pair of islands you may build no bridge, one bridge, or two bridges — never three or more. Bridges only run straight, horizontally or vertically, between islands that line up in the same row or column with clear water between them.
• No crossings. Bridges may never cross each other. A horizontal bridge and a vertical bridge cannot pass through the same point, so once a line occupies a lane, no perpendicular bridge may cut across it.
• One network. When the puzzle is finished, every island must be reachable from every other by walking along bridges. You cannot leave an island — or a little cluster of islands — floating on its own, even if all of its numbers happen to be satisfied.

Controls

To build a bridge, tap one island and then tap a second island in the same row or column — or simply tap the empty lane between them. The first tap draws a single bridge; tapping the same connection again upgrades it to a double bridge; a third tap removes it entirely, cycling none → single → double → none. If you try to add a bridge that would cross one you have already drawn, the move is refused and briefly flashes red, and it is counted as a mistake. The board shows a running timer, a mistake counter, and a connectivity indicator that tells you whether all your bridges currently form one linked network. Islands whose number is already satisfied are dimmed so you can concentrate on the ones that still need work; an island shaded red has too many bridges and must be eased back.

Winning

You solve the puzzle the instant three things are true together: every island carries exactly its number, no two bridges cross, and all the islands are joined into one connected network. At that moment a win banner appears with your time and mistake count, and your score is submitted to the leaderboard. Because each puzzle is built to have a single unique answer, there is always exactly one correct final picture — you never have to guess, and there is never more than one way to be right.

Solving techniques

• Start with saturated islands. An island whose number is large compared with how many neighbours it has often forces bridges. A “4” at the edge of the board with only two possible neighbours must send a double bridge to each of them — there is no other way to reach four. Corner and edge islands are the best place to begin because they have the fewest directions to consider.
• Use the “one less than the maximum” rule. If an island needs almost as many bridges as its maximum possible (two per neighbour), you can usually place at least one guaranteed bridge in every direction. For instance a “3” with two neighbours must have at least a single bridge to each, because a bridge missing on one side could not be made up on the other without exceeding two.
• Avoid isolation. Never complete a small group of islands into its own closed loop too early if that would seal it off from the rest of the board. Even when a cluster’s numbers all balance, the finished puzzle must be one single network, so keep at least one route open to the islands you have not connected yet.
• Watch the crossings. Because bridges cannot cross, a planned bridge in one direction can rule out a crossing bridge elsewhere. When two possible bridges would intersect, work out which one is forced by an island’s count and the other is automatically eliminated — that is often the key that unlocks a region.
• Mark what is certain, then repeat. Fill in every bridge you can prove, update each island’s remaining need, and look again: forced moves cascade. Each certain bridge lowers a neighbour’s remaining count and often creates the next forced move, so steady propagation — not guessing — carries you to the single solution.

Frequently asked questions