The Zotmeister - January 27th, 2006

03:13 pm - Puzzle 26: Island Oasis

There's a delightful puzzle design out there with a long tradition of uninspiring names: the World Puzzle Championships have called it Corral; Nikoli calls it Bag. I was struggling to find a worthy title for it before trying to make my own. As it happened, glmathgrant beat me to it with The Inner Limits. I felt scooped. However, e suggested recasting it as an "island" puzzle, and in so doing unwittingly gave me an idea. As perhaps you've noticed, I like puzzles that present "exceptions to the rules", where the information provided at the onset is not necessarily trustworthy (as in Smullyanic Dynasty, where givens can lie) or where some element has a version that works differently (as in Seeking Syren, where one of the "potential nodes" is really Syren). I was able to find a way to squeeze that concept into this design, and it consequently gave me a title. I hereby present an original variation of this classic design. Echolocation fans should be particularly fond of this.

The monochromatic grid on the left is an unsolved Island Oasis puzzle; the largely-familiarly-shaded version on the right is the unique solution to that puzzle. I could say I made the oasis a different shade of blue because it's fresh as opposed to salt, but I'd be lying: I made the oasis a different shade of blue because I could and I felt like it, and for no other reasons.

Mangled together from the instructions to Echolocation and Islands in the Stream: Each cell of the grid is either "water" or "land"; the objective is to determine which for all cells. The land cells, which form the "island", must ALL be orthogonally contiguous; each water cell must be part of an orthogonally contiguous cluster of water cells incident on the outer border of the grid EXCEPT for exactly one - the "oasis" - which must be completely surrounded by land cells (including diagonal adjacencies). Cells containing numbers are land; each number is the quantity of land cells orthogonally radiant from it, including its own cell.

Also mangled together:

1) Each cell of the puzzle 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 cells and shading the water cells as you go along.)
2) Each numbered cell is land. (No need to put dots in them.)
3) Think of the numbers as land surveys. Each number is how many land cells exist total between the one it's in and either the outer border or the first water cell it encounters in each of four directions (up, down, left, right). This total includes the cell the number is in, but not any water it's aligned with - the numbers are stricly land-only counts.
3) All the land cells must form a single "island". That's right - all of them; there's only one island in this island puzzle. All land cells in the grid must be orthogonally contiguous (a single polyomino).
4) Somewhere on the island is a freshwater oasis; in puzzle terms, there is a single water cell in the grid completely surrounded by land. All eight cells adjacent to this oasis - including diagonally - are land. It wouldn't be fresh if it were incident on the ocean, now, would it?
5) Apart from the oasis, no water may be enclosed by the island. There can't be any place you could draw a freehand loop around one or more non-oasis water cells where every point of the loop is on land, including sides and corners of land cells. Equivalently, if you were a fish in an arbitrary non-oasis water cell and could only swim from cell to cell up, down, left, and right one cell at a time (NEVER diagonally), you must be able to reach the outer border without crossing land.

Remember the oasis is always a single cell. This fact means that much of the logic that applies to the standard version of this puzzle still functions here. One rule in particular that still holds is extremely valuable, and despite just how important it is to the puzzle, I explain it here anyway:

( How to solve the sample puzzle )

Let me know what you think. I'm running low on prizes at the moment, but send in your solution anyway and maybe I'll scrounge up something. - ZM