PUZZLE TECHNIQUES

HASHI SOLVING TIPS

We are going to Build Bridges and learn techniques to solve Hashiwokakero or Hashi puzzles. This puzzle consists of islands that are all connected to each other via bridges (=horizontal or vertical lines).

Below you will find the explanation of several techniques and tips to make Building Bridges puzzles faster and easier.

4 IN CORNER, 6 AT A SIDE OR 8 IN THE MIDDLE

An island in a corner can have a maximum of 2 neighbors and a maximum of 2 lines per bridge. So if island 4 connects in a corner, then you must connect this with both neighbors via a double bridge.

With island 6 on one side you follow the same reasoning. Here there are 3 neighbors, so you get 3 double bridges.

Finally a Hashi puzzle with island 8 always has 4 neighbors with double bridges.

ISLANDS WITH 1 NEIGHBOR

If islands 1 or 2 have only 1 neighbor, you can immediately place the correct bridge, namely a single bridge at island 1 and a double bridge at island 2.

3 IN CORNER, 5 AT SIDE OR 7 IN THE MIDDLE

We do not know exactly which bridges to install, but we do know the following:

• 3 in corner: definitely a single bridge to both neighbors.
• 5 at side: certainly a single bridge to the 3 neighbors.
• 7 in the middle: certainly a single bridge to the 4 neighbors.

Below you see 5 connected to 3 neighbors by a single bridge and 7 connected to 4 neighbors by a single bridge.

Since there is certainly a bridge running from 7 to ?, you now know that A and B cannot be connected directly to each other.

SAME SITUATION BUT WITH 1 AS A NEIGHBOR

We have about the same situation as the Hashi puzzle above, but now we know that one of the neighbors is island 1. So we automatically know that the other bridges must be double.

ISLANDS WITH A FEW NEIGHBORS

The fewer neighbors islands have, the easier it is to find their bridges.

Below island 4 only has 2 neighbors, 2 on the right and 6 on the bottom. So you know that you can place a double bridge to both.

AVOID ISLOLATION OF ISLANDS

One of the main rules of solving Hashi puzzles is that all the islands must be connected to each other. You must therefore prevent isloation.

If you connect islands 1 below, they are isolated from the other islands. This is not correct. So you can connect both islands with absolute certainty to their other neighbor.