kaht: well.... the same holds true for a rubik's cube though, there's like 2 billion possible combinations for it, but if you switch just one cube around, it can become unsolvable.
Okay. I have
got to chime in on this.
When operated in accordance with the rules of operation, a Rubik's Cube is demonstrably solvable. Always.
When you
break the rules (and rotating a corner block clearly breaks the rules), then those rules
stay broken. In the revised-rules scenario, the Cube is still solvable (re-rotate the block, or just disassemble and reassemble the Cube).
So, it's a bit of misdirection to declare the Cube unsolvable, unless you also allow a rule to be broken temporarily and then the game re-engaged with the rules re-established.
It would be the same thing if we started playing a game of chess, then in the middle of the game (or earlier, if I want a chance, because I really suck at chess), I replace all my non-kings with queens and all your non-kings with pawns and then said "
Now let's see you win!" We see
that as bogus logic, don't we?
Sorry for spinning off on that, but if it's any consolation, I waited until the
second time I read it before responding.
Regarding the specific puzzle in this thread, I'm pretty sure solvability is a real factor. For example, this puzzle cannot be solved following the rules:
Code:
_________
|[2][1][ ]|
|_________| <-- pretend this row isn't a row
There are topological proofs driving this conclusion. I'm pretty sure that larger iterations of the same problem are constrained by the same rules. However, we are lulled into thinking there's a solution because there are so many millions of moves that an obviously-unsolvable situation isn't apparent.
So, it's possible that a given configuration really
could be impossible.
Near as I can tell from reading the code, the numbers are assigned positions at random. Based on this, I would suggest that there will be solvable and unsolvable combinations served indiscriminately. How yucky.
Now, you know what would be
really delicious? Write a routine that starts with the known 6x6 block "solved" and creates a sequence of legal consecutive moves (1000 ought to be sufficient) at random, and then applies them, and
then shows you the resultant cube. You don't even have to remember the moves: just repeat a thousand times {pick a random tile adjacent to the hole and move it into the hole}.
Let's face it, if you
knew the problem was solvable, you would be much more interested in solving it, wouldn't you...
Cheers,
![[monkey] [monkey] [monkey]](/data/assets/smilies/monkey.gif)
Edward
"Cut a hole in the door. Hang a flap. Criminy, why didn't I think of this earlier?!" -- inventor of the cat door