Common Bridges Puzzle Mistakes, and How to Avoid Them
Six mistakes that trip up Bridges (Hashi) players, from over-building and missed crossings to closed pairs and guessing, and how to backtrack calmly.
The most common mistakes in Bridges (Hashi) are building more bridges than an island's number allows, reaching past the nearest island, drawing or overlooking crossings, closing off a pair or group of islands too early, and guessing. Each one has a quick check that catches it. This guide goes through six mistakes with small diagrams, then shows how to backtrack to your last sure move instead of starting the puzzle again.
It is written for players who know the rules. If you are new, how to play Bridges covers them in a few minutes.
Mistake 1: building past the number
Over-building means giving an island more bridges than its number. It usually happens when you draw a double bridge out of habit, or when you count the bridges on one side of an island and forget the other.
A typical case is an odd number in a corner. A 3 with two neighbours looks as if it wants double bridges, but two doubles make four.
The correct reasoning is that a 3 with two neighbours is one short of full: it must send at least one bridge to each neighbour, and the third bridge is still undecided. Draw the two single bridges and leave the third until the puzzle tells you where it goes. The Hashi strategies guide has a table of these "one short" numbers.
The check: when you finish with an island, count every bridge touching it, in all four directions, and compare with the number. Doing this once per island takes a second and catches most over-building at once.
Mistake 2: counting the printed number, not what is left
The printed number on an island is where it started. Once it has bridges, what matters is how many more it needs. A 5 with three bridges is effectively a 2 for the rest of the puzzle, and a neighbour that is already complete is no longer a neighbour at all.
Solvers who forget this make two kinds of error. They miss forced moves, because a 4 that still needs one bridge and has one open neighbour does not look forced if you still think of it as a 4. And they over-build, because they plan bridges for the full number again.
The habit that fixes it: whenever you add a bridge, update the "still needs" count of both islands in your head, and treat complete islands as finished. On paper, tick or shade an island when it is complete; Wikipedia's article on Hashi suggests marking completed islands as a way to avoid errors. Then look around: the islands next to the one you just completed have lost a neighbour.
Mistake 3: reaching past the nearest island
A bridge can only connect an island to the first island it meets in a straight line. It cannot jump over an island, and it cannot run diagonally or bend round a corner. Beginners sometimes plan a bridge to a distant island that happens to be in the same row, without noticing another island in between.
The same thing applies when you count neighbours. If you count the 3 as a neighbour of the 2 in this diagram, your sums will be wrong and every deduction based on them will be wrong too.
The check: for each island, look along the row and column in all four directions and stop at the first island. Those are its neighbours. Nothing further away counts.
Mistake 4: crossing bridges, and missing the blocks they create
Bridges may never cross, and this rule causes two different mistakes. The first is drawing a bridge across one that is already there. The second is quieter and far more common: drawing a bridge and not noticing what it now blocks.
In the diagram, the 3 on the left and the 2 on the right of the middle row could see each other before the vertical bridge was drawn. Afterwards they cannot. If either island had only one other neighbour, its bridges are now forced, and a player who misses the block will search the board for a move that is sitting right there.
The check: after every long bridge, run your eye along its whole length and look for pairs of islands on either side of it. Each such pair has just lost a link, and each of those islands has one fewer neighbour.
Mistake 5: closing off a pair or a group
The rule that every island must join one network is the one most often broken by accident. The classic version is joining two 1s: the single bridge completes both islands, and the pair is cut off from everything else. Joining two 2s with a double bridge does the same.
Bigger groups can close too, and that is harder to spot. The puzzle below has six islands. The second diagram shows a fill that satisfies every number and has no crossings, yet it is not a solution.
Where did it go wrong? The 2 at the top has one neighbour, so its double bridge to the 4 is forced. The 2 in the bottom-right corner has one neighbour too, so it takes a double bridge from the 3. The mistake is the next step. The 4 needs two more bridges, from the 1 on its right and the 2 below. A double bridge down completes the 4 and the bottom-left 2, and with the top 2 already complete, those three islands are sealed off. So the 4 must send one bridge to the 1 and one down. The rest follows.
The check: before you add the last bridge to an island, ask whether it, and every island joined to it, will still have a way out to the rest of the board. The connectivity rule covers this in depth, including a quick way to count what a group still needs.
Mistake 6: guessing
Guessing means drawing a bridge you have not proved, in the hope that it works out. In Bridges it is costly, because a wrong bridge rarely fails at once. It changes neighbour counts, blocks crossings and completes islands, and the contradiction often turns up many moves later, far from the bridge that caused it.
A well-made Bridges puzzle never needs a guess. It has exactly one solution, and there is always a next move you can prove. Every Puzzle Picnic puzzle is built that way: a solver checks that it has one solution, and logic alone gets you there.
There is a legitimate tool that looks a little like guessing: what-if reasoning. You pick one undecided bridge, imagine it, follow only the moves that are then forced, and look for a broken rule. If you find one, the opposite is proved. The difference is that you never commit to anything unproved. Keep these chains short; if one runs for more than a few steps, look for a simpler move first.
The check: before you draw a bridge, say to yourself why it must be there. "The 1 has no other neighbour" is a reason. "It looks right" is a guess.
The six checks at a glance
Each mistake above has a check that takes a second or two. Run the ones that fit as you go, and most errors are caught before they can spread.
| Mistake | Quick check | When to run it |
|---|---|---|
| Building past the number | count every bridge at the island, all four sides | when you finish an island |
| Counting the printed number | say what the island still needs | after every bridge, for both ends |
| Reaching past an island | stop at the first island in each direction | when you list neighbours |
| Crossings and missed blocks | look along the new bridge for islands on both sides | after every long bridge |
| Closing a pair or group | ask whether the group still has a way out | before the last bridge on any island |
| Guessing | name the reason the bridge must be there | before every bridge |
Two of the checks belong to every bridge you draw: updating what both islands still need, and naming the reason the bridge must be there. If you only adopt two, take those.
How to backtrack without starting over
When a puzzle goes wrong, you rarely need to clear the whole board. Go back to the last bridge you can prove and solve forward from there. This routine finds that point quickly.
- Look for broken rules first. Count the bridges at every island and compare with the numbers. Look for any island with too many, any crossing, any pair with more than two bridges, and any closed group.
- Find islands with no way to finish. An island that still needs bridges but has no open neighbour left is a sure sign that an earlier move was wrong.
- Remove bridges near the problem, newest first. Take away bridges around the broken island one at a time, and for each ask whether you can still prove it from what is left.
- Stop at the first bridge you can prove. Everything up to that point is sound. Everything after it is suspect, so remove those bridges too.
- Solve forward again, slowly. Use the checks from this article on each new bridge. The mistake usually shows itself on the second pass.
In Puzzle Picnic you also have three free hints a day, and a hint explains the next logical step. That makes a hint a good way to learn which deduction you missed. A solve that used hints or power-ups is marked as assisted rather than clean, so you can always tell your own solves apart. Nothing runs out while you think: your time is recorded, but there is no countdown.
Frequently asked questions
Why can't a bridge go where I want it?
Something is in the way. A bridge cannot cross another bridge or pass over an island, it can only run straight across or down to the nearest island in that direction, and no pair of islands can have more than two bridges.
My grid looks complete. Why is it not solved?
Check that every island is joined into one network. It is possible to satisfy every number and still split the board into separate groups. Trace a route from one island to every other; if one cannot be reached, a group closed off somewhere.
Should I start again or try to fix a wrong puzzle?
Usually fix it. Look for the broken rule, then remove bridges near it, newest first, until you reach one you can prove. Starting again only makes sense if you cannot tell which of your early bridges were proved.
Is using a hint a mistake?
No. A hint that explains the next logical step teaches you the deduction you missed, which is the fastest way to stop missing it. Leaning on hints while a level is new, and using fewer as it becomes familiar, is a sensible way to learn.
Which mistake should I fix first as a beginner?
Counting the printed number instead of what is left. Once you think of every island by what it still needs, over-building and missed forced moves both become much rarer.
Where to go next
Pick one check from this article and use it on every bridge in your next puzzle, then add another. The Hashi strategies guide shows the deductions that keep a solve moving, the story of Hashiwokakero explains where the puzzle and its rules came from, and when you are ready you can play Bridges and put the checks to work.