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Hashiwokakero - Bridge Building Puzzles

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How to solve Hashiwokakero puzzles successfully

Hashiwokakero are puzzle games where the player must connect a given configuration of islands by drawing horizontal or vertical bridges between them so that every island has a number of bridges equal to the number specified inside the island's circle and all islands are connected (directly or indirectly) between them. The bridges cannot intersect between themselves and no more than 2 bridges can be drawn between any pair of islands.

Based on the rules of the game some progress can be made by trial and error, but there are some common patterns presented below that will speed up the game's progress once identified and acted upon.

One way connection

One way connection

Islands that have a neighbor on only one direction out of the possible four (north, west, south, east) need to be connected to it as there is no other possibility to put that particular bridge on the island. Based on the number of bridges it can be a single or double bridge for that particular direction.

Do not connect islands of 1 between themselves

Do not connect 1s example

If an island with 1 bridge has multiple connecting choices but only one of those choices is with another island having >= 2 bridges, then that connection should be chosen. Otherwise we would end up with two islands of 1 connected with each other and they would have no connection possible with the other islands. This would violate the problem contraint of having all the islands connected between themselves (directly or indirectly).

Number 8

Number 8 example

Since there are only 4 directions possible for the bridges (north, west, south, east) and we can have at most 2 bridges for each direction, it is not possible to have more than 8 bridges from the same island. Therefore, whenever we see the number 8 inside the circle of an island, we can draw all possible bridges from it and make sure that they will exist in the puzzle's solution.

Number 7

Number 7 example

An island with a value of 7 implies that from the eight possible bridges, one is missing. This means that every direction still has at least one bridge, we just don't know exactly where there are two of them and where we have a single one. Therefore it's always safe to draw bridges, one for each direction, and explore later which are the ones that need to be doubled.

6 bridges with special neighbors

Six bridges with special neighbors

Sometimes an island with 6 bridges has special circumstances which allow us to apply the solution encountared for 7 or 8 bridges. For example, if there are neighbors on only 3 out of 4 directions, then all bridges need to be drawn and doubled as that's the only way to obtain 6 bridges from 3 directions. Another case is when one of the neighbors is a 1. This implies that we have 5 bridges remaining for the other 3 directions, and since 2 directions, doubled, ensure only 4 bridges, this means each direction needs to have at least one bridge.

Conclusions

We've presented above some patterns that will help you solve Hashiwokakero puzzles once you identify them and react accordingly.

If you want to practice what you have learned you can click the button below to start a new puzzle game. Good luck!

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