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This page lists useful techniques for solving Hashi.


Guaranteed BridgesEdit

If there is an island with (2) that has only one island it can join to, it must be double in that direction. Similarly, all bridges must be double from a (4) with only two directions, a (6) with only three and an (8) period.

Partial GuaranteesEdit

A (3) with only two neigbours must have at least one bridge to each of them. Similarly, a (5) with three neighbours and a (7) period must have at least one to each neighbour. It's worth drawing these in because it can form walls that force other bridges into place.

ReductionEdit

1 4 2
3
1 4 2
|
3

If an island can only have a certain number of bridges in one direction, it can be "reduced" to one of the above cases. For example, in the scenario shown, the (4) can only have one bridge to the (1). This effectively turns it into a (3) with two neighbours, hence the bridges shown on the right.

IsolationEdit

Remember that all the islands have to be joined together, so you can't place bridges where it'll isolate any islands. The simplest example is that you can't connect two (1)s together because they would be isolated together.

AssumptionsEdit

The most powerful technique, but often the slowest. You assume a bridge is drawn in (it's usually easiest to draw a faint dotted line) and see what the repercussions are. It's usually helpful to start with outrageous assumptions, for example the fact that bridges rarely extend for a large number of length units. Once your assumption is made, proceed with the puzzle as normal – but make sure you continue to use faint lines! There are three possible outcomes of an assumption:

  1. You end up solving the puzzle. This is rare unless it's an easy puzzle, or if you've already solved most of it.
  2. You hit an impossibility. This is the outcome you're aiming for. If you get a problem, say an island with bridges blocking all sides, you know the assumption was incorrect. For a well-chosen assumption, this can be very useful.
  3. Your assumption grinds to a halt and you are forced to make either a secondary assumption in addition to the current one (not recommended if you can avoid it) or an entirely new one.

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