How To Solve Hashi Puzzles - step 1
The best way to learn how to solve Hashi puzzles is to actually solve them, and in this tutorial we'll look at a puzzle and work through every step. Here's the puzzle:
Although it's a pretty simple example, the techniques you learn here will help you with every Hashi puzzle you ever come across. Here goes!
Just Enough Neighbours
Remember you're trying to draw bridges between these islands, and the bridges must follow these rules:
- They must be vertical or horizontal (no diagonals or wiggly lines)
- They can't cross other bridges
- You can't have more than two bridges along any one route
Look at the (4) at the bottom-right of the board. It's size 4, so it needs four bridges. But it only has two neighbour islands - one to the North at f9 and one West at i7. So if you're only allowed two bridges on any route, the only way to lay out enough bridges is to have two pointing North, and two pointing West.
This is the Just Enough Bridges technique.
(By the way, do you see how we've greyed in the (4) in the second board? That's to tell us that we've 'solved' this island - i.e. found all the bridges - and we can stop worrying about it. This is a great way to mark your progress - when all the islands are filled, the board is solved!
There's another example of Just Enough Bridges right next door, the (6) at i5, so we can fill in two bridges each to g5 and i3.
One Unsolved Neighbour
This is actually an easier case of Just Enough Neighbours. The island at h4 - a (1) - has only one neighbour it can reach, the (2) at h2. So its bridge has to go there - there's nowhere else to go!
Now, look what has happened. By drawing the bridge from h4 to h2, we've cut off part of the board. The (3) at i3 now has only one more island it can reach - i1. Since this island needs another bridge (it's size 3 and so far only has two bridges) the last bridge must be pointing to i1.
Based on this rule, we can work out where to put the second bridge for island h2. Where should it go?
Few Neighbours
Few Neighbours is another rule based on the fact that you can only have two bridges on any route. Look at this board:
Do you see that g3 (size 3) has only two neighbours it can reach? And since you can only have up to two bridges per route, it must be the case that at least one bridge goes out in each direction. (We don't know where the third bridge goes, yet).
Using a combination of this technique, plus One Unsolved Neighbour, plus Just Enough Neighbours, we can solve a fair chunk of the board. In fact, we can get this far:
Now what?
Leftovers
That simple rule, no more than two bridges on any route, has helped us get surprisingly far - and it can help us again.
Look at the Island (4) at c5, above. It needs another two bridges to complete and has two neighbours, but one of them (at e5) is a (1) and so can only support one bridge. So at least one bridge must go East. (Perhaps both do, we don't know yet - we'll find out in the next section).
So with the Leftovers technique, you can see that even if we used up all the available bridges on all the other available islands, we still need to have one bridge pointing to the (2), like this:
We've nearly solved the puzzle! In the next section, we'll look at how to finish it off, thanks to the rule of Isolation