Hashi Step Two - Isolation

Isolation is one of your most powerful tools when trying to solve Hashi puzzles. Remember, every island must be able to reach every other, and armed with this fact you can solve even the hardest Hashi puzzles!

Take a look at the puzzle. It's nearly solved but now seems to be stuck - we don't know whether the (4) at c5 has two bridges going East or one bridge each going East and South. Which one is it?

The key is the island at e5, the (1). It only can only have one bridge, but what would happen if the bridge went East?

If the bridge went East, then the two (1)s in the middle would become isolated. They would form a short circuit, cutting themselves off from the rest of the board!

So we know that the island (1) at e5 cannot point its bridge East - so it must point North, to c5.

From here there's only one move left - a bridge from the (2) at c7 to the (1) at e7 - and the board is solved. You're a genius! Have a beer.

Complex Isolation

If isolation was that easy to spot all the time then where would be the fun? Here are a couple of rather more tricky cases to give you an idea what to look out for.

The islands shown in green represent one large interconnected 'chain'. It wraps around the board, but now there's only one point where it could connect to the rest of the islands - via a bridge from the (4) at m10 to the (3) at k10.

So although there are two potential bridge routes out from the (4) - one going North to k10 and one going East to m12 - we have to go North to stop the chain from becoming isolated.

Here's an even more complex example from further on in the same puzzle. The green island chain has become even longer, but now again there's only one point at which it can connect to the rest. This time it's not immediately obvious. What should be done?

Look at the (3) at g8: it needs one more bridge to complete. If that bridge went South to the (4) then you would complete the (3) and the (4) - but then the (4) wouldn't have any more bridges available to connect West to the rest of the board. So the last bridge from the (3) can't go South - it must go West, to g6. Then the (4) can connect West to i6 and the whole board will be joined.

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