Hashi solving strategies
CloseStart with bridges you can deduce with certainty. Each connection changes the options in the puzzle and may reveal your next clue.
These techniques work for Hashi, also known as Hashiwokakero or the bridges puzzle. If you are new to the game, first read the rules.
The drawings illustrate connections and parts of puzzles. They are not exercises to complete.
Getting started
Identify available neighbours, build certain bridges and avoid isolating islands.
Strategy 1
Count the neighbours you can actually connect
Look horizontally and vertically. In each direction, you can only reach the first island: an island behind it does not count.
Rule out paths blocked by other bridges and islands that cannot accept any more connections. For example, a 1 island can never take a double bridge.
Strategy 2
Look for islands that need all their possible bridges
If an island needs as many bridges as its available neighbours can provide, all those connections are required.
At the start, a 2 with just one neighbour needs a double bridge. The same applies to a 4 with two neighbours, a 6 and three or a 8 and four: two bridges to each, provided those neighbours can accept them.
Strategy 3
Build certain bridges first
A 3 with only two neighbours needs at least one bridge to each. If it left out either neighbour, the other could only provide two bridges, leaving it one short.
The same idea applies to a 5 with three neighbours and a 7 with four. You can build one bridge to each neighbour without yet deciding which connections will be double.
Strategy 4
Count the missing bridges
After each change, subtract the bridges already built from the island’s number. A double bridge counts as two.
If a 4 already has three bridges and only one available neighbour remains, the last bridge must go to it. Check that neighbour too: the new bridge may force another connection.
Strategy 5
Avoid closing off groups too soon
All islands must form a single network. If other islands remain in the puzzle, two 1 islands cannot be connected to each other: they would both be complete and isolated from the rest.
You also cannot complete two 2 islands by joining them with a double bridge if other islands remain outside. Apply this check to any group. Before completing it, make sure it can still connect to the outside islands. If only one possible exit remains, that exit is required.
Going further
Combine clues from several islands and look for required connections between groups.
Strategy 6
Count what the other neighbours can provide
Not every neighbour can provide two bridges. Count how many each one still needs, and whether you have already used one of the two bridges allowed between that pair.
In the drawing, if the 4 did not connect to either 3, the other two neighbours could only provide 1 + 2 = 3. Therefore, it needs at least one bridge to each 3. We do not yet know whether it will use the 1.
This calculation can also force a double bridge: a 4 with three neighbours that can accept 1, 1 and 2 bridges needs all those connections.
Strategy 7
Anticipate paths that will be blocked
A new bridge can remove an option from another island, even one far from its endpoints.
Here, the 1 can only see the 4 on its right: that horizontal bridge is required. The vertical connection between the two 2s is ruled out because it would cross it.
Now each of those 2s has just one available neighbour on its right. Both need a double bridge to that neighbour. One deduction has led to two more.
Strategy 8
Find a group’s only exit
As well as checking individual islands, look at groups. If a group can only connect to the rest through one pair of islands, that connection is required, even if bridges are still missing within the group.
In the drawing, the group on the left can only exit through the top 3 towards the 2 on its right. Leaving that path empty would split the puzzle into two networks.
One more clue: single or double?
If the group has only one possible exit pair, add up its numbers. Each internal bridge counts twice, once at each end; each outgoing bridge counts once.
If the sum is odd, the exit must be single. If it is even, the exit must be double: zero bridges would isolate the group. Here, 2 + 3 + 2 + 2 = 9, so the exit is single.
This deduction requires exactly one possible exit pair. It cannot determine individual connections when there are several exits.
Hard puzzles
When direct counting is not enough, follow the consequences of an assumption.
Strategy 9
Look one move ahead
If direct counting is not enough, make a specific assumption: “What if there were no bridge here?” or “What if it were double?” Follow only the connections that assumption would force.
You can rule it out if an island can no longer reach its number, a crossing appears or a group has no possible connection to the rest. If you find no contradiction, the assumption remains open: that does not prove it is correct.
For example, in strategy 7, assuming a vertical bridge would leave the 1 without any legal connection. That consequence is enough to rule out the vertical bridge.
If you make temporary changes to the puzzle, remember what they are and undo them before trying another assumption. “Check solution” counts as an attempt in the game; you do not need to press it to reason through a possibility.
When you get stuck
- Check which islands have fewer options after your latest bridges.
- Count what is missing, taking completed neighbours and blocked paths into account.
- Check that no group has been left without an exit to the rest.
You can mark islands you think are complete to keep track of your solving. Marks are your own aid: they do not check whether the solution is correct.
If you are unsure where the next bridge goes, check your previous connections before adding one just to try it.
Put it into practice
Try these ideas on the daily puzzle. You can choose a difficulty and start with Very easy.