**1. Divide the grid into rectangles (squares count as rectangles) along the grid lines in accordance with the following rules.**

2. Every piece must contain exactly one symbol (+, -, or |).

3. Every piece containing a + must be square. Every piece containing a - must be wider than it is tall. Every piece containing a | must be taller than it is wide.

4. No four pieces may meet at a corner.

2. Every piece must contain exactly one symbol (+, -, or |).

3. Every piece containing a + must be square. Every piece containing a - must be wider than it is tall. Every piece containing a | must be taller than it is wide.

4. No four pieces may meet at a corner.

## 6 comments

given a a puzzle, how can you verify that it has a solution?

Um. . . by solving it? :P

If you're asking how to write a computer algorithm to do so, then I can't help you.

I have a feeling he means "While constructing a puzzle, how can you verify that it has a unique solution?" But stop me if I'm putting words in your moth, Alejandro.

The answer, I guess, would be to construct the puzzle as you would solve it, by creating a series of moves that can be the only move.

I misread the puzzle and thought that you are given some +s and -s and |s on a grid and then you would add segments until 1,2,3,4 are satisfied.

So my question was: how can you build a puzzle, with the +s and -s and |s and know that there is at least one solution for placing the segments?

(sorry, I don't get email notifications of replies. you can find me at my blog http://alejandroerickson.com)

I misread the puzzle and thought that you are given some +s and -s and |s on a grid and then you would add segments until 1,2,3,4 are satisfied.If by segments you mean unit-length line segments connecting vertexes of the grid's square lattice, then, uh, thatiswhat you're supposed to do. It's not a misunderstanding. :/how can you build a puzzle, with the +s and -s and |s and know that there is at least one solution for placing the segments?If all you care about is there beingasolution, as opposed to exactly one solution, one way is to divide the grid into rectangles which satisfy the tatami rules, and then place an appropriate symbol in each rectangle.Again, though, if you're asking how to program a computer algorithm to determine whether a given puzzle has a solution or not, then that is beyond the scope of my knowledge and of this blog. Consider joining the Grey Labyrinth forums at www.greylabyrinth.com and asking your question there (although honestly, I can't figure out what your question even is). There are a zillion smart folks on there who could generate a discussion on the matter.

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