Hashiwokakero, often abbreviated to Hashi, and also sometimes called Bridges, is a logic puzzle originating from Japan.
The puzzle is played on a square grid. The size of the grid determines the level of difficulty. Here is an example of a small Hashi grid:
As you can see, the puzzle comprises a number of circles with numbers inside. These are called islands. The objective is to connect all the islands by drawing a series of bridges between them. Here’s what that puzzle looks like once it’s been solved:
Small Hashiwokakero puzzles like this are easy to solve. But as the grids get bigger, the puzzles can get a lot tougher!
To solve a Hashiwokakero puzzle, you'll use a combination of logic and the numerical clues given. It's about gradually deducing where bridges can and cannot be, based on the constraints provided by the puzzle.
As with many logic puzzles, practice helps you recognise patterns and strategies more quickly.
Here are some tips to help you get going.
Start with islands with only one possible connection. Look for islands that have only one way to satisfy their number requirement. For example, if there's an island with a '1' and only one neighbouring island, you know where that bridge must go. Islands in the corners of the puzzle can often provide a good starting place as they are restricted to bridges in only two possible directions.
Consider islands with maximum bridges. If an island has a '4' and it's on an edge, then you know two bridges must go out from both available sides. If an island has an '8', it means it's surrounded on all four sides by two bridges each.
Avoid over-connecting. Keep track of the number of bridges each island has. If an island needs only one more bridge, you can't connect it to an island in a direction that would necessitate two bridges.
Use other islands to deduce bridge locations. Sometimes, the positioning of other islands can prevent possible bridge connections. If two islands could be connected by two bridges but there's another island in the way, you know they can only be connected by one bridge.
Ensure island interconnectivity. Avoid creating isolated clusters of islands. Every island must be connected in a network. If you see a potential cluster forming, think about how it will connect to the other islands.
Make safe assumptions and test them out. In more complex Hashi puzzles, you might reach a point where it's not immediately clear what the next step is. In these cases, it can be helpful to make an assumption and see how it affects the rest of the grid. If you reach a contradiction or an impossible situation, you'll know your assumption was wrong. If you try this, ensure you remember your steps so you can backtrack easily.
Use a process of elimination. If you're unsure about where bridges should go, consider where they can't go. Often, by eliminating impossible bridge placements, the correct placements become clear.
Continuously check for completion. As you're drawing bridges, keep checking islands to make sure their bridge requirements are being met. If you've met the bridge requirement for an island, move on to focus on the others.
Review your solution. Once you believe you've solved the puzzle, take a moment to review it. Make sure all the islands meet their number requirement. Check there are no bridges crossing each other. Verify all the islands are interconnected and there are no orphans.
Like all logic puzzles, the more you practice Hashiwokakero, the better you'll become at solving them. Over time, you'll develop an intuition for bridge placements and will recognise patterns more quickly.
Remember that patience is key. Some puzzles can be tricky, and it might take time before you see the solution. But with each puzzle you solve, the process becomes a bit more intuitive.
Want to try your hand at Hashi? We have options! We sometimes include them in our free Puzzle Weekly magazine – you should totally sign up for that if you haven’t already, as it puts 28 brand new puzzles in your inbox every week.
You can also find four levels of Hashi puzzles in our Jumbo Adult Puzzle Book – which happens to include more than 500 puzzles of 20 different varieties.