# Puzzle 14: Seeking Syren - The Zotmeister

#### solving the puzzle of life one entry at a time

## Aug. 11th, 2005

### 02:44 pm - *Puzzle 14: **Seeking Syren*

*Seeking Syren*

First, a quick note: I'm being far too generous posting this one now, given how I *still* haven't received a solution for my previous puzzle yet, I *know* that one's easy, and it's been about three-and-a-half weeks! I suppose this puzzle may well have a greater reward than that last one, though, so you may want to concentrate on this one first. I gave away an A. T. Cross pen and pencil set to the first to solve my first *Smullyanic Dynasty*; I wonder what I could give away to the first to solve this...

There's a certain sameness of design to a lot of the sort of puzzles I like to solve and construct; under the hood, their mechanics are the same as or similar to each other. Most of them are binary determination puzzles - that is, every cell of a grid is either one thing or another. Water or land, knight or knave, pillar or open... you get the idea. I decided that I'd like to try to up the ante by introducing third options, at least.

But then I realized that I had another issue - I have a pair of lovely magicians I'm not entertaining, one of which is awaiting her debut. I had the basic idea of what sort of puzzle I wanted to make in their honor, an original idea as far as I know - a maze where the exit is unmarked. The title was a gimme, but some of the bits and pieces of the rules needed to be ironed out. I decided to combine the two concepts and see if they work together. My first attempts at a ternary determination puzzle proved quite unfeasible, but then I thought of a way to make it all work without becoming counterintuitive: color! Testing the resulting design revealed it to be quite robust, fascinating, and unique... and so it is that Zotanna Terran and her partner Syren Lyght now have something to occupy themselves with until I get around to writing an actual *story* involving them.

I hope you enjoy this original design as much as they do.

What, three grids? Don't worry, I'm just providing an additional visual aid. The left grid is an unsolved

The Z-cell is always given; the S-cell is never given. Each remaining cell of the grid is either a "node" or an "island cell"; numbered cells must be the latter. All island cells belong to exactly one "island": an

...Wow, now

1) See the 'Z' in the grid? That's Zotanna Terran, our protagonist. See the 'S' in the grid? Of course not - that's why the puzzle is called

2) Zotanna moves as a knight does in chess, "hopping" (for lack of a better term) from cell to cell to Syren, along a path you have to discover. This path can't use any numbered cells. Every cell used in the path between them is a "node". Any cell

3) The 'S' and the nodes must be placed so that there is only a single route Zotanna can use to get to Syren; that route must use each node exactly once. This means, among other things, that there can never be a loop in the node path.

4) Nodes cannot be adjacent to each other, at all, not even diagonally (they may not share sides OR corners).

5) Any cell not part of the path is part of an "island". Islands are polyominoes that each include exactly one of the numbers you see in the grid. That number is how many cells are in that polyomino. This makes them just like the islands in

6) Unlike

7) If you fill in all the cells that start blank - marking the 'S' and all the nodes, and coloring the rest - without breaking the above rules, you've solved the puzzle! [The path from node to node will be obvious, and by the rules it will be unique, so drawing it in is not required.]

...Yikes. It's not as bad as it seems at first glance, but it definitely may take some getting used to, so feel free to read this:

(Start of sample puzzle solution)

The key to solving this puzzle is to work back and forth as necessary between the path and the islands. Trying to do only one or the other will likely get you stuck until you switch.

I'll label the cells with coordinates: the rows are A-E from the top down, the columns 1-5 from left to right. I'll start with an island; the red '2' in A1 needs another cell in its island, and with that red '5' two cells below it in C1, it can't use B1 - that would connect the two matching-color numbers, violating rule 6 as I numbered them. So A2, being the only other choice, must be red.

If I try to place another island next, I'll have trouble. However, if I look at the path, it'll be easy: since Zotanna starts in a corner, e has only two places to go from there, and one of them has a number in it. This means C2 is the first of the three nodes in the path. Marking it with a circle, it blocks off the options of that red '5' quite nicely, defining its island as C1-D1-D2-E2-E3. This, in turn, defines the green '3' on D3: it can't go up given the green '4' on B3, so it must go right to D4, and from there, given the green '1' on E5, E4 is off-limits so the last cell must be C4. Wow - that's eight of the seventeen blank cells filled in; we're almost half-way there already! See, this isn't so bad, right?

Now I look at the path again. It has two options to travel in - the next node can be A3 or B4. But see what would happen if A3 were the node? Look at the green '4' on B3. It needs to use A3! It would be stuck with only three cells if A3 were blocked by a node. Marking B4 as a node, the rest of the path is now obvious: the only valid move from there is to D5, and lastly Syren must be in C3.

With the path completed, all that remains is to finish up the islands, and there are only two of them. Since every remaining blank cell in the grid needs to be used, B1 and B2 must be green - as only the green '4' on B3 can reach them. That completes the last green island (you

(End of sample puzzle solution)

If you

I'm rather amazed at this first offering - it's fairly tricky. Feel free to comment here on the design as well as this particular construction, and of course, I try to pull out the best rewards for my original puzzle designs, so email me what solution you come up with; my email address and privacy policy are on my user info page. - ZM

What, three grids? Don't worry, I'm just providing an additional visual aid. The left grid is an unsolved

*Seeking Syren*puzzle; the center grid is the solution to that same puzzle. The right grid clearly shows "Zotanna's path", which I'll explain.The Z-cell is always given; the S-cell is never given. Each remaining cell of the grid is either a "node" or an "island cell"; numbered cells must be the latter. All island cells belong to exactly one "island": an

*n*-omino containing exactly one numbered cell, and that number is*n*; islands whose numbers are matching colors may not be orthogonally adjacent. Nodes may not be adjacent to each other (orthogonally or diagonally), and must comprise a linear and unambiguous path of chess knight's moves connecting the Z-cell to the S-cell that must pass through all nodes. The puzzle is solved when the Z-to-S path and all islands are defined....Wow, now

*that*is concise. I don't blame you for using this list to figure out what in the name of sanity you're supposed to do here:1) See the 'Z' in the grid? That's Zotanna Terran, our protagonist. See the 'S' in the grid? Of course not - that's why the puzzle is called

*Seeking Syren*. You have to find her, and show Zotanna how to get to her. Think of it as a logic-puzzle version of hide-and-seek on an astral plane that was never meant to fly.2) Zotanna moves as a knight does in chess, "hopping" (for lack of a better term) from cell to cell to Syren, along a path you have to discover. This path can't use any numbered cells. Every cell used in the path between them is a "node". Any cell

*not*part of the path is*not*a node. The cells Zotanna and Syren are in are not nodes, either. I recommend placing a circle in cells you've determined to be nodes, and an 'S' in the cell Syren is hiding in when you find it. Incidentally, that number*under*the grid is the total number of nodes in the solution. It's nothing you couldn't figure out yourself with a little arithmetic, but I figured I may as well save you the time.3) The 'S' and the nodes must be placed so that there is only a single route Zotanna can use to get to Syren; that route must use each node exactly once. This means, among other things, that there can never be a loop in the node path.

4) Nodes cannot be adjacent to each other, at all, not even diagonally (they may not share sides OR corners).

5) Any cell not part of the path is part of an "island". Islands are polyominoes that each include exactly one of the numbers you see in the grid. That number is how many cells are in that polyomino. This makes them just like the islands in

*Islands in the Stream*, and I gave them the same name for that reason, but there is one difference - these islands are colored. I suggest coloring in each cell of an island to match the color of its number, or writing in the initial of the color ('R', 'G', or 'B') if you prefer that. [I have "dented" the corner of each numbered cell based on their color - each color has a different corner dented - so that the colorblind will have an easier time telling them apart.]6) Unlike

*Islands in the Stream*, islands*may*touch each other along cell sides, but only if they are*different colors*. Islands of matching colors may touch at corners, but not along their edges.7) If you fill in all the cells that start blank - marking the 'S' and all the nodes, and coloring the rest - without breaking the above rules, you've solved the puzzle! [The path from node to node will be obvious, and by the rules it will be unique, so drawing it in is not required.]

...Yikes. It's not as bad as it seems at first glance, but it definitely may take some getting used to, so feel free to read this:

(Start of sample puzzle solution)

The key to solving this puzzle is to work back and forth as necessary between the path and the islands. Trying to do only one or the other will likely get you stuck until you switch.

I'll label the cells with coordinates: the rows are A-E from the top down, the columns 1-5 from left to right. I'll start with an island; the red '2' in A1 needs another cell in its island, and with that red '5' two cells below it in C1, it can't use B1 - that would connect the two matching-color numbers, violating rule 6 as I numbered them. So A2, being the only other choice, must be red.

If I try to place another island next, I'll have trouble. However, if I look at the path, it'll be easy: since Zotanna starts in a corner, e has only two places to go from there, and one of them has a number in it. This means C2 is the first of the three nodes in the path. Marking it with a circle, it blocks off the options of that red '5' quite nicely, defining its island as C1-D1-D2-E2-E3. This, in turn, defines the green '3' on D3: it can't go up given the green '4' on B3, so it must go right to D4, and from there, given the green '1' on E5, E4 is off-limits so the last cell must be C4. Wow - that's eight of the seventeen blank cells filled in; we're almost half-way there already! See, this isn't so bad, right?

Now I look at the path again. It has two options to travel in - the next node can be A3 or B4. But see what would happen if A3 were the node? Look at the green '4' on B3. It needs to use A3! It would be stuck with only three cells if A3 were blocked by a node. Marking B4 as a node, the rest of the path is now obvious: the only valid move from there is to D5, and lastly Syren must be in C3.

With the path completed, all that remains is to finish up the islands, and there are only two of them. Since every remaining blank cell in the grid needs to be used, B1 and B2 must be green - as only the green '4' on B3 can reach them. That completes the last green island (you

*did*remember to mark A3 as green, right?); the last blue island uses everything else left, and the puzzle is solved.(End of sample puzzle solution)

If you

*still*don't get it, well, try one of my several other puzzles [scroll down] instead.*Islands in the Stream*in particular should be a good warmup for this. Incidentally, when I get emailed an incorrect "solution", my standard procedure is to point out what makes it incorrect, so if you're just a little uncertain, go ahead and try, and if one of us made a mistake, I'll point it out. That goes for any of my puzzles, not just this one.I'm rather amazed at this first offering - it's fairly tricky. Feel free to comment here on the design as well as this particular construction, and of course, I try to pull out the best rewards for my original puzzle designs, so email me what solution you come up with; my email address and privacy policy are on my user info page. - ZM