User login
Impossible Sliding Puzzle?
September 14, 2009 - 11:41am
I'm working on the hardest of the three sliding puzzles for Monday. I've completed the entire image except for a 2x2 square in the bottom right. Two tiles are switched, and I believe it is impossible to switch them. I looked it up on Wikipedia and other resources, and exactly half of randomly generated n-puzzles are impossible to solve.
So this leaves me wondering how this site creates the puzzles. Does it start with a completed puzzle and shuffle the pieces? This would guarantee that every puzzle created on this site is possible to complete successfully. However, if the tiles are scrambled and randomly placed, then half of all permutations would be impossible.
If the pieces are positioned randomly, I would like to see one of three things. First, and maybe best, a way to re-scramble the puzzle and start from scratch. Second, the automatic saving option removed so everyone always starts from scratch (this wouldn't be optimal, as these can take time). Third, and probably most difficult, the code be rewritten so that every puzzle is solvable.
If I'm wrong about the way this is generated, I apologize. Please correct me.
Thanks.
September 14, 2009 - 12:06pm
#2
I believe the algorithm is already designed to prevent unsolvable puzzles. I'll ask the developer to weigh in here on that.
September 14, 2009 - 1:21pm
#3
This puzzle is solvable.
An option to start over would be nice. I like that the puzzle is saved (and not timed) because many things can happen to interrupt the game - phone calls, dog barking, getting the kids off to school, etc.
September 14, 2009 - 1:42pm
#4
Taz,
I'm sorry you're having difficulty! On the other hand, it ::is:: the hardest Slider puzzle after all. :-P
I did look into the math when creating the puzzles. Rather than just randomly swapping tiles around - which would certainly lead to a bad puzzle half the time - I perform parity swaps with the missing tile's position.
Some brilliant mathematicians have proven that if you color the tiles like a checker board, and always swap the missing tile with its opposite color, the puzzle is still solvable. This works from any solvable state - not just the starting position - provided the board is re-colored before every swap. This is the approach that I took, and I'm convinced that it works!
You are correct to say that finding a case where two adjacent tiles are swapped is an unsolvable predicament. Funny story! The newsprint article that you see bits of in the background is taken from an February 17, 1880 (Wow! That's old!) article of the Rochester Democrat and Chronicle about this very puzzle! About that time, a mischievous Sam Loyd marketed a physical version of the slider puzzle, assembled in one of these unsolvable configurations, along with a $1000 reward for anyone who solved it. It drove people mad!
I took the liberty of looking at your save state (because, you know, us game wizards can do that sort of thing!), and it turns out saphir23 was correct - the three tiles that belong in the upper left look very similar, and you have one of them out of place. That misplacement does have additional tiles in between - the out of place tile is not directly adjacent to where it belongs - so you're still good! I assure you it is solvable!
If you pay special attention to the texture of the clouds - and apply liberal use the "H" key to view the unscrambled image (there's no penalty for doing so!) - you should be able to see what we mean. I chose the images for the OMG-level Sliders to be challenging - but still solvable. If it were easy, everyone would have the Gold Achievement!
I will look into adding a "re-scramble" button - but I encourage you to give it another go! Who's to say rescrambleing would leave you in any different of an endgame? You've got the entire left side of the puzzle solved! Why throw out all that work!?
In this case, I recommend treating the right-hand portion of the puzzle as a 2 x 5 sub-puzzle (i.e. - Don't touch the 3 x 5 portion on the left!) and solve it from there. You can do it!
Thank you for your posting! I hope you are enjoying the game! (And just wait until you see some of the later weeks' OMG Slider Images ... Mua hahahahaha! >:D)
- Joe
PTI's Flash Developer
September 14, 2009 - 3:24pm
#5
Cool, thanks for making sure they're all solvable. I'll give it another shot. Maybe I did manage to miss two- the two in the top right look very similar. I'm usually an expert on these things, so it isn't that I can't do it. I could do these in my sleep.
September 14, 2009 - 3:25pm
#6
Yepp. Took ten seconds to fix once I realized my error. Thanks again!
September 14, 2009 - 4:45pm
#7
Man! Are you guys Geeks!!! LOL I did not GET any of the explanations and it must be because I am a figurative thinker, not a literal (logical) one, I have tried so many way to fix both the med and hard puzzles that I have turned myself inside out, lol! I would like to start from scratch myself with the puzzle as it was placed and use all the advice that has been given, is there a way to do that oh wise and intelligent puzzle master (ok, looking for brownie pts here, lol, and if flattery helps...) seriously though, I have got it so turned around, I can't see what's up or down anymore. (Frustrated Sigh) HELP! LOL Micci
September 16, 2009 - 1:15am
#8
Best Advice:
Start in one corner and build that column/row, then build the next column/row. The last two column/rows will need to be solved together, just start on one end and work to the other. Those clouds were tricky if you didn't look too close. Keep trying, you'll get it.
September 17, 2009 - 12:54pm
#9
I had the same problem. Thanks to this post I can now enjoy the rest of my day! :)
September 18, 2009 - 12:14am
#10
I have 1 more small bit of advice... when I got caught I had my son join me... I will never do a slider alone again... Bring it Joe... we have 2 pairs of eyes :)
but in all seriousness... I would say it was just another set of eyes but the extra perspective was an amazing help!
You might have a tile misplaced -- a couple of them look very similar!