Rules
Hashi is played on a grid of numbered circles called islands. You join them with bridges. The number on each island says how many bridges end there.
- Straight lines. A bridge runs across or down to the next island in that direction. It can’t turn or pass over an island.
- One or two. Two islands can share a single bridge or a double. A double counts as two.
- No crossing. Bridges never cross each other.
- Match the numbers. Every island ends up with exactly its number of bridges.
- One group. When you’re done, you can walk from any island to any other along the bridges.
The puzzle from this guide, solved. An island turns teal once its number is met.
Loops are fine: a group of islands can close a circle. What breaks the rules is a second group that never joins the first. Every Hashi on PuzzleKite has exactly one solution, and you can reach it by logic alone. You never need to guess.
First moves
Every first move is counting. A link between two islands holds two bridges at most, and never more than the smaller number, so a link to a 1 holds one. Compare what an island still needs with what its links can still hold. On PuzzleKite, Easy grids need nothing else.
Exact fit Easy
When an island needs exactly as many bridges as its links can still hold, there’s no choice left: fill every link to the top.
The 4 in the corner has two neighbours: the 3 to its left and the 5 below. Two links at two bridges each hold four. That’s its number, so both links take a double.
At least one each Easy
Sometimes a number is too big to leave any link empty. If an island needs more bridges than the rest of its links could hold with one link left out, every link gets at least one bridge.
The 5 below the corner has three neighbours. Leave any one link empty and the other two hold four bridges at most, one short. So every link gets a bridge. The double from the corner is already there. Add a single to the left and one down. The fifth bridge comes later.
The same counts work on any island. The table assumes every neighbour can take a double:
| Open neighbours | Exact fit | At least one each |
|---|---|---|
| 1 | 1 or 2 | – |
| 2 | 4 | 3 |
| 3 | 6 | 5 |
| 4 | 8 | 7 |
A corner island has two directions to look in, an island on the edge has three, and one in the middle can have four. A 1 next door holds only one bridge, so an island beside a 1 fills up sooner: a 3 with a 1 and one other neighbour is an exact fit too.
Closed links Easy
Every bridge you draw changes what’s around it. A link closes for good when a bridge crosses its path, or when the island at either end is finished. When an island has one open link left, everything it still needs goes there.
- The new single from the 5 runs under the 3, so the 3’s link down is closed.
- The 3 has a double to the corner and needs one more. Its only open link goes left, so draw it.
- Now the 4 needs three more. The 1 in the corner holds one and the 5 below holds two: an exact fit. The finished 1 closes its link down.
Forced links Medium
Counting looks at a whole island at once. Medium grids also need you to look at one link at a time. Add up what an island’s links could still hold, then take one link away. If what’s left can’t reach the number, that link needs at least one bridge.
The 4 on the right edge has three neighbours, and neither first move works: 4 isn’t more than 2 × 2, and its links could hold five. But the 1 below holds only one bridge.
Without the link to the 2 on its left, the 4 could reach at most 2 + 1 = 3 bridges. So that link gets one.
Forced links turn up next to small numbers. A 1 or a 2 caps the links around it, so the island beside it leans on its other links. When Hint finds one of these, it says an edge link is forced: edge is the maths word for a link.
Isolation
The last rule, one group, gives the hardest moves. A closed group is a set of islands whose numbers are all met, with no bridge leading out. Unless it holds every island, a closed group splits the board, so it can’t happen. Hard grids make you try a bridge in your head and ask: would this close a group?
Closed groups Hard
Look at the 2 on the left edge. It has three neighbours: a 1 above, a 2 to its right and a 1 below. Neither counting nor a forced link settles it, so try the link to the right both ways.
The 2 has to take both 1s. All three are finished, and nothing else can reach them.
The two 2s are finished as a pair, and nothing else can reach them.
Neither extreme works, so the two 2s share a single bridge.
The middle case is worth remembering on its own: two 2s never take a double between them, because the pair would be finished and cut off. The check works on bigger groups too. Before you finish an island, look at what it’s joined to, and make sure the group still has a way out.
Two 1s never meet Hard
The smallest closed group is two 1s joined to each other. Both are finished, and nothing else can reach them. So a link between two 1s always stays empty.
Common mistakes
Almost everyone makes these at first. Each one has a simple fix.
Crossing a bridge
A long bridge is easy to draw straight through another one. Before you draw, check what already runs across its path.
Joining two 1s
It finishes two islands at once, which feels like progress. It also cuts them off. Two 1s never share a bridge.
Trusting teal
Teal means an island’s number is met, not that it’s joined to the rest. Follow the bridges from a teal island and make sure they lead somewhere.
Doubling on a hunch
If counting forces only one bridge, draw the single and come back for the second. A wrong double is hard to spot later.
The 3 needs one more bridge, but the link down to the 2 crosses the single between the two 5s. Check calls it a mistake straight away.
Every number is met, but the two 1s at the bottom right joined each other. The board is split, and Check marks them red.
Next steps
Once counting feels quick, move up a level. Each one adds a new idea.
- EasyCounting onlyExact fits, at least one each, closed links.Play Easy →
- MediumAdd forced linksOne link an island can’t do without.Play Medium →
- HardAdd isolationNo closed group before the end.Play Hard →
The same ideas carry every size. When 7×7 feels quick, try 10×10, then 13×13. Want the board from this guide? Open it in the game and solve it from the start.