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Lizely

Hashi Bridges Puzzle

Connect six numbered islands with non-crossing single or double bridges while matching every clue and forming one network.

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How to use

  1. 1.Use the arrow keys to move to the nearest island in a row or column; the island you left becomes the bridge anchor.
  2. 2.Press Space or Enter to cycle that eligible connection through one bridge, two bridges, and no bridge.
  3. 3.Match every island clue without crossings and connect all six islands into one network, then Restart to replay.

About Hashi Bridges Puzzle

Hashi Bridges is a compact implementation of Hashiwokakero, the Japanese logic puzzle about connecting numbered islands. Six islands appear on a five by five field. Each number tells you the exact count of bridge lines that must touch that island. Move between aligned islands with the arrow keys. The previous island becomes the anchor, the new island becomes the selection, and Space or Enter cycles the bridge between them from none to one, one to two, and two back to none.

A valid solution must satisfy all of the core rules at once. Bridges can join only the nearest visible islands in the same row or column. No pair can carry more than two bridge lines. Bridges cannot cross one another, and they cannot pass through another island. Every island must receive exactly its printed number of bridge lines. Finally, all islands must belong to one connected network rather than separate completed groups. These rules follow Nikoli's official Hashiwokakero description and the independent Bridges documentation in Simon Tatham's Portable Puzzle Collection.

This page uses a deterministic six-island ladder board. The top-left and top-right clues are two, the middle pair are three, and the bottom pair are two. Seven legal single bridges solve it: three horizontal rungs plus the two vertical segments on each side. The fixed fixture is intentionally small enough to complete entirely by keyboard while still testing clue totals and whole-network connectivity. The puzzle layout and 100-points-per-bridge score are Lizely choices, not universal Hashi difficulty or scoring standards.

The browser maintains a map from each allowed island pair to a bridge count of zero, one, or two. Every change recalculates the degree of all six islands. It also constructs an adjacency graph from active bridges and walks that graph to prove that every island can be reached from the first. Segment geometry checks any horizontal and vertical lines for an interior intersection. A board is complete only when all clue degrees match, the graph is connected, and no crossing exists.

Overfilling any clue is reported immediately as a contradiction. For example, cycling an already satisfied connection to a double bridge can push an island above its printed total. That state is recoverable because you can cycle the offending bridge again, but it proves the current arrangement cannot be a solution. The interface freezes only after correct completion. The automated fixture checks clue values, edge eligibility, bridge cycling, degree sums, graph connectivity, crossing geometry, an overfilled deadlock, and the full seven-bridge keyboard-equivalent completion sequence.

Each island announces its clue and current bridge degree to assistive technology. The selected island has a visible outline. Bridge paths are rendered with text line glyphs inside the CSS grid, and every surface, border, accent, foreground, and warning uses site theme variables. No canvas, external image, sound, pointer precision, or downloaded level is required. Arrow navigation selects the nearest aligned island in the requested direction, making the complete board playable without a mouse.

The score equals 100 times the active bridge-line count. Completing the intended seven single bridges earns 700 points. Best completed score may be stored only in localStorage for this game; it is not uploaded or tied to an account. Restart clears all bridges, moves, selection history, score, and completion state. Press Escape twice within 400 milliseconds for the shared simulated-spreadsheet boss screen, and repeat it to return. Use Hashi as a short deductive network puzzle. For related grid logic, try Hitori Puzzle, Minesweeper, 15 Puzzle, or Maze Game.

Methodology & sources

A fixed set of six islands and seven eligible nearest-neighbor edges defines the puzzle. Each edge stores 0, 1, or 2 lines. Validation sums incident lines per island, rejects degrees above or unequal to clues, checks horizontal/vertical segment intersections, and breadth-first traverses active edges to require one connected component. Score is 100 times active bridge lines.

Frequently asked questions

What does an island number mean?
It is the exact total number of bridge lines that must touch that island; a double bridge counts as two.
Can bridges cross?
No. Horizontal and vertical bridges may not cross, pass through an island, or connect non-aligned islands.
Is matching every number enough?
No. In addition to exact clue totals, every island must be part of one connected network.
How do I remove a bridge?
Select the same aligned pair and cycle it: none becomes one, one becomes two, and two returns to none.

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