Bridges
How to solve Bridges (Hashi): five moves, no guessing
Updated Tuesday, October 27
To solve a Bridges puzzle, start with the islands whose number can only be met one way, then draw every bridge an island cannot do without: each bridge you draw blocks the ones that would cross it and brings the next island into view. Every Gridarium puzzle can be finished this way, without guessing.
The rules
Islands are circles with a number. Join them with bridges: straight lines, across or down, between two islands that see each other with nothing in between. A pair of islands may carry one bridge or two. Bridges never cross a bridge or an island. Each island's number is the total of bridges touching it, and when you finish, every island must be reachable from every other.
Step 1: islands with no choice
An island that sees only one other island sends all its bridges there. An 8 in the middle sends two bridges each way; a 6 on an edge and a 4 in a corner do the same. In general, when an island's number equals twice the number of islands it can see, every pair gets a double bridge.
Step 2: at least one each way
A 3 that sees two islands must send at least one bridge to each: if one of them got nothing, the other would need three, and two is the most a pair can carry. The same holds for a 5 with three neighbours and a 7 with four. Draw those single bridges now; the doubles come later.
Step 3: what a bridge blocks
Every bridge you draw cuts the line of sight between the islands on either side of it. Islands that used to see each other across it no longer can: cross those possibilities off, and recount the islands that lost a neighbour. Often one of them is now an island with no choice.
Step 4: nothing gets cut off
Two 1s facing each other never link: a bridge between them would complete both and leave them cut off from everyone else. The same goes for two 2s joined by a double bridge. More generally, a group of islands whose numbers are all met must still have a way out, unless it is the whole puzzle.
Step 5: one careful trial
When nothing else moves, pick a possible bridge and imagine it drawn. Follow steps 1 to 4. If an island ends up unable to reach its number, or a group is left cut off, that bridge was impossible. One step is always enough on Gridarium.
The three levels
- Easy: 7 by 7, about 10 islands. Steps 1 and 2 are enough.
- Medium: 9 by 9, about 16 islands. Steps 3 and 4 come into play.
- Hard: 12 by 12, about 28 islands, where step 5 is sometimes needed.