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!

- The number inside an island indicates the maximum number of bridges that can connect to that island.
- Bridges can only be drawn horizontally or vertically, never diagonally.
- Two islands can be connected by one or two bridges. There can never be more than two bridges between any two islands.
- Bridges cannot cross over other bridges or islands.
- Bridges must run in a straight, uninterrupted line between the islands, with no turns.
- At the end of the puzzle, all islands must be interconnected, meaning you can travel from any island to any other island via the bridges, without having to jump across any gaps. In other words, no island or group of island can be left separate.

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. Similarly, if you see two '1's next to each other, they *cannot* be connected because they would form a separate group that could not be reached from the rest of the puzzle. So if either, or both, only have one other neighbour, you know that you must connect to it. Our example puzzle has two 1s that cannot be connected together – here they are again:

Because they cannot connect to each other, we can deduce that the top 1 *must* connect to the 2 to its left, and the bottom 1 *must* connect to the 3 to its left. There aren't any other possibilities.

*Consider islands with limited connection options*: An island with a '3' in a corner must have at least one connection both horizontally and vertically. A '4' in a corner must have two bridges connecting in both directions. A '5' on an edge must have at least one connection in every valid direction, and a '6' on an edge must have two bridges in every direction. A '7', wherever it appears, must have at least one bridge in every valid direction. Similarly, an '8' anywhere in the puzzle must have two bridges in every direction. Putting in these known connections may not solve an island completely, but the bridges will block other parts of the puzzle and therefore help decide where other bridges can and cannot go.

*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. For the same reason, avoid bridges that would isolate islands. Our example puzzle has a possible bridge like that:

If we were to connect the highlighted 1 and 2 together, they would isolate the two 1s to the right, making it impossible to complete the puzzle. That means the 1 at the top *must* connect to the 4 to its left, and the 2 at the bottom *has to *connect to the 3 in the corner.

*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 method, it can be helpful to do so by marking bridges with a different colour (if possible). That way, if you come unstuck and realise you have made an error, it's easy to remove all the bridges in the new colour and return to the point prior to making the assumption.

*Mark off completed islands.* When an island has its full complement of bridges, it's helpful to put a cross through it, or shade it in, or use some other method of marking it as complete. This helps you to focus on the parts of the puzzle that still need to be worked on.

*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.

If you have a Kobo eReader with stylus, you can grab our *Hashiwokakero For Stylus Devices*, which is designed specifically for it.