Forums

Number: Puzzle #250
Genre: Archipelago
Author: Maarten
Appeared at: June 15, 2007

I am absolutely perplexed at how to go about this puzzle. I've filled in the bridges around the edges, a few short segments on the inside that no other bridges could block, and two horizontal bridges in the bottom right where a vertical bridge would cause an impossible layout.

I haven't really had any trouble with the other Archipelago puzzles, but none of the usual attacks are working on this one. I'm thinking it has something to do with what I like to call "boxing", which is where a subset of islands can only be connected to each other with only a few possible connections to the rest of the group, which generally forces a specific bridge as an "exit". However, the subsets I can see (in the checkerboard pattern in the center) have too many exits to check simultaneously.

Any help would be greatly appreciated, but if the break-in makes the rest of the puzzle a piece of cake, a gentle nudge in the right direction would be preferable.

On a more positive note, I'm really enjoying this type of puzzle, despite my usual avoidance of the type of logic it relies on

I don't know if you have already done this, but one thing that often helps to open up Archipelagos is this:

If an archipelago puzzle has N islands, then it needs N-1 bridges to connect them all. If you count what the largest number of bridges is that can be fit into the puzzle, then often (including in this case) that number is exactly N-1. (I've been trying to create puzzles where this is not the case, but that is pretty hard to do.)

Then, you can look at every "lake" (region of water that is completely surrounded by islands, or more precisely, region whose potential bridges cannot interfere with any other potential bridges) individually and see in what ways the maximum number of bridges can be placed in that region.

In this particular case, you can see that in the top left "lake" there is only one way to fit 5 bridges (excluding the one at the very top), so you know they all have to be there.

I hope this helps.