November 10th, 2005 - The Zotmeister
solving the puzzle of life one entry at a time
Nov. 10th, 2005
03:09 pm - Puzzle 20: Archipelago
Once upon a time there was a clever little puzzle named Islands in the Stream. And it was good. There was also this neat little puzzle named Block Party. And it was fun. Then one day, apparently some evil scientist wanted to see what their offspring would look like, and created Archipelago: the bastard cousin of island puzzles. Although many concepts are familiar, the rules are just different enough to really screw with the head of someone who's been solving other puzzles.
The grid on the left looks like it could be an Islands in the Stream puzzle, but don't be fooled: it's an Archipelago puzzle. The grid on the right is the unique solution. (If you were to try to solve it as an Islands in the Stream puzzle anyway, you may find it would have two solutions. Only two cells remain ambiguous, but that's all it takes to invalidate it.)
Each cell of the grid is either "land" or "water"; the objective is to determine which for all cells. Every land cell belongs to exactly one "island": a rectangle of land cells that contains at most one numbered square and, if it has a number, as many squares total as that number. Islands may never be orthogonally adjacent, but ALL islands MUST be diagonally contiguous. The water cells must contain no numbers and comprise no solid 2x2 squares ("pools").
"...What the?! Now e's saying 'diagonally contiguous'? What has gotten INto Adam?!"
Yeah, well, like I said, it screws with people's heads. Here, I'll try to sort it out for you:
1) Each cell of the grid is either a "land" cell or a "water" cell. Fill them all in to solve the puzzle. (Rather than using colored pencils, I recommend simply dotting the unnumbered land squares and shading the water squares as you go along.)
2) Each numbered cell is land. (No need to put dots in them.)
3) For each number, there is one "island" of land cells. In this puzzle, islands are strictly rectangular, so for each number you need to portion off a box whose area is that number. Islands may not have multiple numbers.
4) Each land cell is a part of one and only one island; islands cannot overlap, nor can they touch each other EXCEPT at their very corners.
5) ALL islands must be connected into a single "archipelago", such that all are diagonally contiguous. In other words, not only CAN the islands touch at corners, but they HAVE to, such that one could travel from any arbitrary island to any other staying on land by solely passing through island corners.
6) No "pools" are allowed: you can't have four water cells making a two-by-two square anywhere in the puzzle. Even if it's part of a larger rectangle of water cells, it's still a pool and it's still illegal.
Note that there's no restriction on having an island WITHOUT a number. That's part of the puzzle: you may find that in order to prevent pools and to keep the archipelago connected, you may find the need for an island (of deducible area) to be in a numberless spot. Don't forget that ALL ISLANDS MUST BE RECTANGULAR, even unnumbered ones - that's how you can deduce the unique solution!
( How to solve the sample puzzleCollapse )
I was surprised how easy it was to make these, especially the sample puzzle - making a useful Block Party sample, in comparison, was far trickier. Hopefully this one will get you thinking. My email address is on my User Info page if you'd like to share your solution with me. I have the occasional habit of sharing something in return. Any generic comments about the design itself can be posted right here. But hey, don't blame me - it's not my original design. I figure someone at Nikoli was having a VERY BAD DAY when e came up with this one. - ZM
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