I have a new addiction, I play Untangle to often, and i am wondering what is the mathematics behind it.
some free games: (but be warned highly addictive)
the rules are simple:
You are given a number of points, some of which have lines drawn between them. You can move the points about arbitrarily; your aim is to position the points so that no line crosses another.
in some versions the difficulty is enriched by making 1 to 3 points unmovable.
This simple puzzle gives rise to all kinds of topological questions:
- is there an algorhitms to solve them?
Some of the games in the android download I was unable to solve, and that makes me wonder, probably there are unsolvable untangle puzzles (so that in any situation some lines will cross)
- how can you recognize them?
- what are the minimal cases of unsolvable puzzles?
- are there fundamentaly different cases of unsolvable puzzles?
Are there any mathematical reports written about these puzzles?
see now back trying to solve one.....