Polygon-Puzzle

[MaxistXXL]

Ok, I think its good not to spam in the old puzzle-suggestion-forum.
The idea behind the puzzle is, that one has to arrange a set of little polygons, so that it fits in one big polygon. The detailed description can do some native-english-speaking one.

The questions which have to be answered before we can start to write a puzzle-generator are the following:
1) Which format shall the puzzle-description have got?
2) Which format shall the string containing the solution have got?
3) How complicated should the polygons be?
4) How complicated should the rules be?

to 1)
I think, we could give coordinates in an co-ordinate system, starting at P(0; 0). Then we give the next points, and by rule we decide, that always two consecutiv points and the last and the first point have to be connected. (0;0) (10;5) (10;0) will be a rectangular triangle, and (0;0) (10;5) (5;5) (10;0) a wired rectangle. The same system we could apply to the smaller polygons. In this way, we can could number the corners in order to identify them.

to 2)
No idea, I am sorry.

to 3)
I think we should avoid angular (not horizontal, not vertical) lines, in order to avoid floating numbers. I dont know whats your opinion, but since computers cannot save infinite exact floating numbers (eg 0.1, sqrt(2), ...) we should avoid them imho. Leaving this alone, I dont see any reason to restrict the number of corners, the shape of the polygons or the number of pieces. Maybe its hard to write a solving/creating-algorhythm, but that doesnt count.

4)
In which steps will we rotate the pieces? According to my suggestion of avoiding angulars, we should rotate in steps of 90 degree. I also think, we could mirror the pieces. This could make levels more hard in the end.


Puzzle-generation:
I'm really bad in those kind of things, but what about a easy way:
We create a random polygon. For this we can use some generator for random numbers to generate the coordinates of the polygon (just the x- or y-coordinate of the old point is not allowed to change).
Then, we decide for some "cutting-lines" on the x- and y-axis. Now we just have to calculate, where these lines meet each other and the polygon, and we will have a lot of rectangles and maybe something more.
Of course it is possible to make it more complicated, so we would have a pentagon, hexagon or whatever.

So now I would be glad to know your opinion.

regards
der Maxist

[MaxistXXL]

I thought about the puzzle-description. It seem to be a bad idea, to start at P(0;0), because there are forms not fitting in the first quadrant, if they have to include P(0;0). Just think about the sign of Red Cross.

Additional to 3) is to say, that I think, all points have to be xeN.

Does anyone have got other suggestions?

[adum]

hi maxist. what i'm not sure about is how the pieces fit together exactly. can people place them at arbitrary points, or do they have to be at whole number coordinates? maybe you can draw up a picture to illustrate your idea?

thanks,
adum

[MaxistXXL]

Sadly I'm not sure about this point. I've got an idea, but this would mean a huge effort for the solution verifier. My idea until now would look somehow like this:


To parse the solution one has to combine the corners. So you have to combine corner "0" and corner "4", corner "5" and corner "8", corner "7" with corner "10", and so on. The numbers in the square would be the identifier of the small polygons, and the number outside of the square would be the identifier for the big polygon.
I hope its understandable, what I mean. The problem is, that I dont know how to put this system into a string to submit it via HTML-Get.

Another difficulty would be, either to make the riddles with only one solution, or to check, if a found solution is correct or not. It seem to be simple, but just imagine a unregulary 100-gon...