Hashi:Linkdoku Bridges Puzzle 4.5.0

In Hashiwokakero, a logic puzzle game sometimes known as Bridges/Chopsticks, you take on the role of a ruler of islands. Your task is to connect these islands based on their population size. Smaller islands require only one bridge, indicated by the number "1" on the island, while larger islands need a corresponding number of bridges, as shown on the island itself. As the sovereign of this unified kingdom, it is your responsibility to ensure that all citizens can travel freely between each island.

RULES:

1. Connect islands (the circles with numbers) with as many bridges as the number indicated on the island.
2. There can be no more than two bridges connecting any two islands.
3. Bridges must not cross islands or other existing bridges.
4. All bridges should create a continuous link between all the islands.

Features:

• 720 free Classic Hashi puzzles
• An additional 480 bonus puzzles released monthly for free
• Various puzzle sizes ranging from 6x9 to 14x21
• Assistance with Connectable Island hints
• Visual cues highlighting connected islands
• Undo/Redo functionality available
• Automatic progress saving feature
• Snapshots for complex puzzles
• Backup and restore your game progress to the Cloud
• Diverse selection of beautiful themes
• Support for multiple languages
• In-built timer to track your solving speed

Solution methods:

Solving a Hashiwokakero puzzle relies on strategic decision-making. Once you determine where a bridge must be placed, this action can dictate the placement of subsequent bridges by narrowing down the possible options.

A key principle is that an island displaying numbers like '3' at a corner, '5' along an outer edge, or '7' within its borders necessitates at least one bridge extending in each valid direction. Failure to satisfy this requirement could impede the solution. Similarly, a '4' at a corner, '6' along an edge, or '8' elsewhere must have two bridges going in every direction.

It's customary to mark off or fill in islands that have reached their bridge limit. This practice aids in minimizing errors and in identifying potential connectivity issues that could disrupt the puzzle's solution path.

Certain restrictions apply, such as avoiding situations where a bridge isolates a group of islands from others, thus preventing complete connectivity across all islands.

The complexity of Hashiwokakero puzzles extends to whether a solution can be achieved efficiently. Determining this involves intricate problem-solving techniques and may fall under NP-complete complexity class.