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Puzzle 1: Islands in the Stream - The Zotmeister

solving the puzzle of life one entry at a time

Feb. 7th, 2005

10:33 pm - Puzzle 1: Islands in the Stream

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The left-side grid above is an unsolved puzzle. The grid on the right is the solution to the same puzzle. It's not as complicated as it's about to sound - in fact, you may be able to figure out the rules (or most of them, anyway) just by looking at it. The given solution is the only valid one.

Each cell of the grid is either "water" or "land"; the objective is to determine which for all cells. Every land cell belongs to exactly one "island": an orthogonally contiguous cluster of land cells that contains exactly one numbered cell and as many cells total as that number. The water cells, which form the "stream", must ALL be orthogonally contiguous, contain no numbers, and comprise no solid 2x2 squares ("pools").

Having just accurately and completely described the puzzle concisely, I figure I'll have lost somebody - after all, my last article had a poem about the meaning of a word, which in and of itself was an example of the word and contained specific directions, and I was asked what the word meant by someone who allegedly graduated from college summa cum laude - so for those of you who didn't understand that but wish to add a third digit to your IQ and try the puzzle anyway, here's a breakdown of the rules:

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) For each number, there is one "island" of land cells. If you were a person standing on a number and could only walk from cell to cell going up, down, left, and right one cell at a time (NEVER diagonally), the total number of land cells you could visit without stepping into a water cell must match the number. (This includes the cell the number itself is in.)
4) No island can have more than one number. (You can never connect two numbers together.)
5) Every land cell must be connected to a number (be able to walk to it as in rule 3).
6) ALL the water cells must form a single "stream". If you were a fish in any 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 EVERY water cell in the puzzle without crossing land.
7) 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. In other words, if there's a water cell from which that fish could swim up one, then right one, then down one, then left one without hitting land, you've made a mistake.

I pity those that find those numbered rules simpler to understand than my earlier three-sentence set of instructions.

Try to solve the sample puzzle yourself. If you can't, I'll walk you through it. I'll name the grid rows A, B, C, D, and E for the top down, and the columns 1, 2, 3, 4, and 5 from left to right. Start with the 1s: they are land, and since they can't have any more land next to them (they are islands of one), put water on each side of them. You've now trapped the square in Row D and Column 1 - it can't reach a number, so it must be water. This makes three water squares in an L shape; the square in Row C and Column 2 would form a pool if it were water, so it must be land. That land square must reach a number, and it has only one direction left to go in - to the right. This makes the center square land. Note that it's next to a three. We've just completed that number's island, so put water in all squares surrounding the island (except at the corners - remember, diagonal doesn't count as connecting). This traps another square in the top row - mark that as water as well. If you've been following along properly, you've only got six blank squares left. Now look at the water - it needs to make a continuous stream. Right now it's in three pieces. If you look at the top piece, you'll see that there's only one square left it could flow into. This is Row A, Column 4. Make that water, and you'll see the 2 in the corner has only one square left to grow into - the one below it. Make that land, and since that completes an island, make the square below that one water. The only number left is a 3, and there are only four squares its island could cover - which means that there's only one water square left in the grid... and since we still have two separate chunks of water, that square has to be the Row-4-Column-4 connector. Mark the other two blanks as land and you're done.

You may figure out your own tricks as you go along - that's the best part of the puzzle. If you get stuck, just scan the whole grid with an open but logical mind and eventually you should see the next step. You shouldn't need to make guesses at all.

The real puzzle lies below. Email me your solution if you solve this. Maybe I'll have a prize for you if you're right. Maybe I won't. Feel free to comment about it here, but I will NOT provide hints. It's not that hard, and besides, I don't want to ruin the puzzle for anyone else. (Spoilers in comments will be severely unappreciated.) - ZM