How to Play Bridges (Hashi): Rules and a First Puzzle
The six rules of Bridges (Hashi), what the numbers on the islands tell you, and a small first puzzle solved move by move, with a diagram at each stage.
Bridges, also called Hashi or Hashiwokakero, is played on a grid of numbered circles called islands. You join the islands with straight horizontal or vertical bridges so that each island has exactly as many bridges as its number. Bridges never cross, at most two run between the same two islands, and when you finish, every island is linked into one network. This guide is for complete beginners: the rules first, then a small puzzle solved one move at a time.
The rules of Bridges (Hashi)
Bridges has six rules. A few apps offer variations, but the standard puzzle, from Nikoli's magazines to Puzzle Picnic, uses these:
- Join the islands with straight bridges.
- The number on an island says how many bridges touch it. Not more, not fewer.
- Bridges run horizontally or vertically, never diagonally.
- Bridges never cross each other, and they never pass over an island.
- At most two bridges join the same pair of islands. A pair can have no bridge, a single bridge or a double bridge.
- Every island must end up connected in one group, so you can walk from any island to any other along the bridges.
The publisher Nikoli, which created the puzzle, states the same rules in four lines on its English rules page: connect the islands with as many bridges as the number, no more than two bridges between two islands, bridges cannot cross islands or other bridges, and the bridges form a continuous link between all the islands.
A bridge counts once for each island it touches. A double bridge between a 3 and a 2 counts as two for the 3 and two for the 2. That is why the numbers on a whole puzzle always add up to an even total: every bridge adds 1 at each of its two ends, so the total is exactly twice the number of bridges.
What the numbers on the islands tell you
In Bridges, an island's number is limited by how many neighbours it has, because each neighbour can take at most two bridges. An island with four neighbours (up, down, left and right) can hold at most 8 bridges, which is why 8 is the highest number you will ever see.
| Neighbours | Most bridges possible | A number this high means |
|---|---|---|
| 1 | 2 | a 2 must be a double bridge to that neighbour |
| 2 | 4 | a 4 must be a double bridge to both neighbours |
| 3 | 6 | a 6 must be a double bridge to all three |
| 4 | 8 | an 8 must be a double bridge in every direction |
The first habit of a good solver is to compare the number with what its neighbours can take. When they match, the island has no choice, and you can draw all of its bridges at once. Islands in a corner of the board usually have two neighbours and islands along an edge usually have three, which is why corners and edges are the classic place to start.
A small neighbour lowers that maximum. A neighbour showing 1 can only ever take one bridge, so a 3 whose two neighbours are a 1 and a 2 can hold at most 1 + 2 = 3 bridges. It must take all of them: a single to the 1 and a double to the 2.
Which islands count as neighbours
An island's neighbours are the first islands it meets looking straight up, down, left and right. A bridge cannot jump over an island to reach one further away, so in a row such as 3 . 1 . 2 the 3 can reach the 1 but never the 2.
Count each island's neighbours before you draw anything. Most islands have only two or three, and that small number of choices is what makes the puzzle solvable by reasoning alone. Later in a solve, bridges you have already drawn cut off more neighbours, because a new bridge may not cross an old one.
A first puzzle, solved move by move
The puzzle below has nine islands on a 6 by 7 board. It has exactly one solution, and you can reach it without guessing. Try it on paper first if you like, then follow along.
Moves 1 to 3: the bottom row
Start where there is no choice. The 1 in the bottom-left corner looks right and finds the 5; looking up, it finds nothing at all. With a single neighbour, its one bridge must go to the 5. The 2 near the bottom-right corner is in the same position: nothing above it, nothing to its right, only the 5 to its left. It needs two bridges, so it takes a double bridge to the 5.
Now the 5 has three bridges and needs two more. Its only other neighbour is the 4 above it, so that becomes a double bridge too. (You could also see this in one step: the 5's neighbours can take at most 1 + 2 + 2 = 5 bridges, exactly its number.)
Move 4: two 1s that must not meet
The two 1s on the left can see each other: one sits directly above the other. A beginner's instinct is to join them, but a single bridge between two 1s finishes both islands at once. That pair would then be a closed little group, with no way to reach anything else, and rule 6 says every island must join one network. So the two 1s are never joined to each other.
Each 1 has exactly one other neighbour. The top 1 takes its bridge to the 3 on its right, and the lower 1 takes its bridge to the 4 on its right.
Moves 5 to 7: the top right
The 4 now has three bridges (two from the 5, one from the 1) and needs one more, either up to the 3 or right to the 1. The 3 has one bridge and needs two more, from the 2 on its right or the 4 below it.
Look at what a double bridge from the 3 to the 2 would do. The top 1 would be complete, the 3 would be complete (1 + 2), and the 2 would be complete. Those three islands would form another closed group, cut off from the rest. So the 3 gets only a single bridge to the 2, and its last bridge goes down to the 4.
That completes the 4 (2 + 1 + 1), so the 4 sends nothing to the 1 on its right. The 2 in the top-right corner still needs one bridge, and its only other neighbour is that 1 below it. One bridge down, and the puzzle is solved.
Check it the way you would check any solution: count the bridges at each island, look for crossings, then trace a route from one island to every other. The 3, for example, has one bridge to the 1, one to the 2 and one to the 4.
Three habits that make every puzzle easier
The worked puzzle used only three ideas, and they carry you through most Easy and Medium puzzles.
- Look for islands with no choice. A 1 or a 2 with a single neighbour, or any island whose neighbours can take exactly its number. Corners and edges first, then anything that earlier bridges have boxed in.
- Keep a running "still needs" count. A 4 with three bridges is really a 1 now. Thinking in what is left, rather than the printed number, is how you spot the next forced move.
- Never close a group early. Before you finish an island, ask whether it, together with the islands it is joined to, still has a way out to the rest of the board. Two 1s side by side and two 2s joined by a double bridge are the classic traps.
These ideas, plus several more for harder grids, are laid out one by one in the Hashi strategies guide. The third habit has its own article, because it turns out to be a powerful solving tool: how the connectivity rule solves Hashi.
How to play Bridges in Puzzle Picnic
In Puzzle Picnic, you build a bridge by tapping an island and then one of its neighbours. Tap again to make it a double bridge. The app teaches the same rules as above, and every puzzle has exactly one solution that logic alone will find, so you never have to guess.
The game has four levels, and the board grows with each one:
| Level | Board size |
|---|---|
| Easy | 7 x 7 |
| Medium | 9 x 9 |
| Hard | 9 x 12 |
| Expert | 11 x 14 |
The app also has one daily puzzle a day, the same for everyone, which rotates through its six games, so Bridges comes round as the daily (always at Medium) once every six days. You also get three free hints a day. A hint explains the next logical step, which makes it a good teacher while you learn. If you want to try the game now, Bridges plays in the browser with no account.
What to do when you are stuck
Getting stuck in Bridges almost always means a forced move is hiding in plain sight. Work through this list in order before you consider anything risky.
- Go round every unfinished island and write or picture its "still needs" number.
- For each one, list the neighbours it can still reach. Remove any that are complete or cut off by a bridge in the way.
- Compare: if the neighbours can take exactly what the island still needs, draw everything.
- If the island is one bridge short of that maximum, it must send at least one bridge to every neighbour that could take two.
- Look at each small group of joined islands and ask whether one more bridge would seal it off. If so, that bridge is ruled out.
- Check that no island has more bridges than its number, and that no two bridges cross.
If you still find nothing, something earlier may be wrong. Common Bridges mistakes covers the usual culprits and how to find them without starting over.
Frequently asked questions
Is Hashi the same puzzle as Bridges?
Yes. Hashiwokakero is the original Japanese name, from the publisher Nikoli, and it means roughly "build bridges". Hashi is the short form used by The Times and many apps, and Bridges is the common English name. The history of the names is in the story of Hashiwokakero.
Can a bridge go diagonally or turn a corner?
No. Every bridge is a straight line, either horizontal or vertical, between two islands in the same row or column. A bridge also cannot pass over an island on the way.
Can two islands have three bridges between them?
Not in the standard puzzle. The limit is two bridges between any pair of islands, which is also why the highest island number is 8. Some computer versions let you change that limit as an option (Simon Tatham's free puzzle collection offers a setting for it), but Nikoli's puzzles and Puzzle Picnic use two.
Do I ever need to guess in Bridges?
Not in a well-made puzzle. A good Bridges puzzle has exactly one solution, and there is always a next move you can prove from the numbers and the rules. If you feel you must guess, you have usually missed a forced move or made an earlier slip.
Does it matter which island I start with?
The finished solution is the same wherever you begin, but starting with the most constrained islands saves time. Islands with one or two neighbours, high numbers on edges and corners, and 1s near other 1s give you sure moves straight away.
Where to go next
Once a 7 x 7 puzzle feels comfortable, move up a size and learn one new idea at a time. Hashi strategies walks through the deductions in the order you will need them, and Bridges for sudoku players explains what carries over if you already solve number puzzles. Every Bridges article on this blog is collected on the Bridges topic page.