Hashi

How to Play Hashi

Hashi, short for Hashiwokakero, is a bridge-building logic puzzle played on a grid of islands. Every island carries a number from one to eight, and that number is the exact count of bridges that must touch it. Your job is to connect the islands with straight horizontal and vertical bridges so that every number is satisfied and the whole archipelago ends up as one connected network, so a ferry planner could walk from any island to any other.

Three rules do all the work. A bridge runs only in a straight line between two islands with nothing in between. Two islands can be joined by one bridge or by two parallel bridges, never more. And bridges may never cross each other or pass over an island. In this version you drag from one island toward its neighbour and release to lay a rope bridge; drag the same lane again to double it, and a third time to take it away. You can also tap a bridge to cycle it, or steer entirely from the keyboard with the arrow keys, Enter to start a bridge, U to undo, R to redo and H for a hint.

Each day brings a new chart that is the same for every player on the same UTC date, so you can compare notes with friends, and a larger weekly chart appears once per ISO week. Every chart is built so that exactly one solution exists, which means you never have to guess: if you are stuck, a deduction is waiting somewhere on the board. Island numbers turn brass and gain a tick when satisfied, and take a red tint with a cross when you have given them too many bridges, so progress never depends on colour alone.

Tips and Strategy

• Start with the corners and edges. A corner island with a 2 has only two possible neighbours, so it must send exactly one bridge to each. An island on a side has only three lanes, so a 6 there doubles all three, and a 5 needs at least one bridge in every lane.
• Big numbers are forced by capacity. An 8 touches four neighbours with two bridges each, so every lane is doubled immediately. A 7 needs at least one bridge in all four lanes, and a 3 in a corner needs a double on one side. Count the lanes before you do anything else.
• A 1 beside a 1 is a trap. Two islands that each need exactly one bridge cannot be joined to each other unless they are the only two islands in the network, because that pair would be sealed off from the rest. Spot these early and steer both 1s toward other neighbours.
• Read a lighthouse as a fence. A beam splits the chart in two, and the network has to reach across it. If a lighthouse says 1, exactly one single bridge links the two halves, so every other lane over the beam stays empty. If the lanes still open over a beam can carry only as many ropes as the lighthouse asks for, every one of them is filled to its limit.
• Work around the fog. A fogged island has no number, but its neighbours do. Settle the numbered islands around it first and its count usually falls out of what is left.
• Use the blocked-lane note as information. When the game refuses a bridge and says the ferry lane is blocked, a committed bridge already crosses that path. Every bridge you place removes lanes from the board, and eliminating impossible lanes is half of solving a Hashi.
• Keep the whole network in mind. Islands that finish their count too early can cut a group off from the rest. If a small cluster is completing itself, check that at least one island in it still has a free bridge to reach the others.
• Spend hints like harbour fees. Each chart allows three hints, and each one costs points on the daily and weekly boards. A hint tells you in plain words which deduction is forced, which makes it a good teacher on practice charts where nothing is scored.

What Makes This Hashi Different

Classic Hashi gives you every island's number. Here it is night on the chart table and fog has rolled over part of the archipelago: a few islands show only a question mark. In exchange, lighthouses stand on the rim of the chart. Each one throws a beam across a channel of open water, and its number tells you exactly how many ropes must cross that beam. That is a new kind of clue. Instead of counting the bridges around one island, you count every rope crossing a line through the whole chart, which lets you reason about the top half of the board against the bottom half, or the west against the east. Built ropes catch the light where they cross a beam, and the lighthouse ring turns brass when its count is met.

Under the hood every chart is generated from the date. A seeded generator lays out an archipelago, places the lighthouses and then hides islands in fog one at a time, keeping each fog only if a solver still finds exactly one solution. It keeps fogging until the chart would have more than one answer without the lighthouses, so the beams are never decoration: every chart needs them. Monday and Tuesday charts can be finished by straightforward counting, beams included; later in the week you will need connectivity reasoning as well. The weekly chart is a large fifteen by fifteen board with three or four lighthouses, built for a longer sitting. Solve any chart and the lanterns light along every bridge while the fog lifts to show the hidden numbers, and the streak ledger logs the crossing as a tide table.

A Brief History of Hashiwokakero

Hashiwokakero is a Japanese puzzle type whose name roughly means "build bridges". It was popularised by Nikoli, the Tokyo publisher that also made Sudoku, Slitherlink and Nurikabe household names among logic fans, and it is sometimes sold under the plain English title Bridges. Like many Nikoli puzzles it grew out of a simple observation: a handful of rules on a grid can generate puzzles that range from a coffee-break warm-up to an hour-long deduction marathon. Computer scientists have also studied the puzzle, and finding a solution to a general Hashi board is a known hard problem, which is part of why a good chart feels satisfying to crack.