March 22nd, 2005


Puzzle 4: Smullyanic Dynasty

It started with the name. I have always admired Raymond M. Smullyan, and one day the thought flashed across my mind: there should be a high-quality logic-based pencil puzzle named "Smullyanic Dynasty". I sort of let the idea just sit and brew in my head, bouncing around a few ideas as to what such a puzzle would look like, what sort of rules it would employ. I knew it needed to have something to do with either binary logic on a grand scale or functional string manipulation. With nothing else better to concentrate on than the sidewalk when walking from a parking lot to an arcade recently, I gave it careful consideration, and I had the gist of it just before I entered the front door. What I had was obviously inspired by all the Nikoli puzzles I'd been solving recently as well as Smullyan's works; I had a grid of numbers and a binary-logic rule for determining which are to be shaded in. However, when I started experimenting with the puzzle, I found that it didn't really work. It was missing something; it needed another rule to make uniquely solvable puzzles.

I came to realize that my unintended inspiration provided the perfect answer. Nikoli has no fewer than three different puzzles that all have one ruleset in common (no, not the single, uncrossed loop); Hitori, Heyawake, and (the atrociously-named) Where is Black Cells have different mechanics but one unifying concept that they all adhere to. I tried applying it to my puzzle design, and it did the trick - it worked beautifully. It was purely an afterthought that I found 'Dynasty' is an ideal name for this concept, bringing the design process full circle.

The result is part Hitori, part Smullyan, part Minesweeper, and part something-all-its-own. It is my great pleasure to debut this original puzzle design. I would like to think Mr. Smullyan himself would be honored by this.

You guessed it - before and after. Puzzle on the left, unique solution on the right.

Each cell of the grid is either a "knight" or a "knave". The objective is to determine which for all cells. Knaves never share a side, and all knights are orthogonally contiguous - that's the "Dynasty". A number in a knight is the number of adjacent knaves, including diagonally; a number in a knave is not the number of adjacent knaves, including diagonally and itself - that's the "Smullyanic".

...Okay, fine, be that way - I'll give you a numbered list:

1) Each cell (unit square) is either a "knight" or a "knave". Mark them all to solve the puzzle. (Rather than colored pencils, I recommend simply shading in knaves and putting a circle in knights. For cells with numbers, either circle the number or shade lightly - you'll probably need that number to stay legible!)
2) The Knaves Stand Alone Rule: Knaves are never orthogonally adjacent - that is, they are never side-by-side. They can touch at a corner, but can never share a side in common. (This means that whenever you find a knave, you know all orthogonally adjacent cells are knights.)
3) The Dynasty Rule: All knights are orthogonally contiguous - just like the water squares in Islands in the Stream [see rule 6].
4) The Smullyanic Rules: Each cell is said to have a "domain", consisting of itself and all adjacent cells, including diagonally. When a cell has a number in it...
- 4a) Knights always tell the truth: ...and the cell is a knight, the number MUST correctly state how many knaves are in its domain.
- 4b) Knaves always lie: ...and the cell is a knave, the number MUST incorrectly state how many knaves are in its domain. (Remember that this includes the knave itself.)

So how can one even start a puzzle where none of the given information can apparently be trusted? Well, there are a few ways. I'll give you two of them in my walkthrough of the sample problem:

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Neither of those two rules will help you with the puzzle below. You should be able to find another rule or two to give you a place to start, however. This puzzle is actually rather straightforward, although I've put a little bit of trickiness into its endgame. For this first challenge, I decided to simply be kind and put a number into every cell; don't expect this to always be the case in the future. I hope you enjoy solving this; as always, tell me what you think on the comment page, and email me the solution if you solve it. - ZM