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1st time ever you play solvable 15 GEM Puzzle with random EmptyX cell (as of 27/10/2017)

In Game:
1 click or 1 touch to move the blank
2 licks or 2 touch to show tile's number
3 clicks or 3 touchs to show original cam

After winniing:
2 clicks or 2 touch to replay
1 clicks or 1 touch to replay backward/forward

Up comming rlease will feature auto-solving by human simulation: rearrange 1st row, then 2nd row, then 3rd row, then 4th row.
This is not optimal but surely give an acceptable solution in realtime for such 'evil' configuration like this
1 5 9 13
2 6 10 14
3 7 11 15
4 8 12

Project Members:

• おとめ座 ひなたぼっこ (admin)

If you argue that AI can solve this problem easily.
Your research is incomplete.
Not only you but also Wikipedia and many others, who cry out that N puzzle can easily be solved by AI.
The fact is that, the theory argument based on PARITY. So you can calculate the permutation or PARITY of the system to make sure, it is a serious matter.
I am not the only one to critics AI emphasize in this problem.
I suspect that PARITY matter can not be solved simply by reducing total taxicab distance. As you are doing by path finding AI algorithm.
With the above configuration, you can see that all AI algorithm navigate to the left, then right, then again left and right and never come up to a result.
The above configuration is only one of many human discovered configurations, not a computer generated.
I am and other in my side ready to PUBLICLY argue here against Wikipedia in this problem, and criticizes Wikipedia and AI community in this problem.
The only pratical solution, up to now, is a "real-time" solution, where it solves each row and column sequentially simulating an ordinary people.
My slightly adjusted problem is here Puzzle Cam download | SourceForge.net[^]
Look forward to you reply

[おとめ座 ひなたぼっこ]

My assessment, BFS or any path finding algorithms is suitable for linear approximation. Like how the cost have been calculated. In general, It may be applicable to b puzzle which is not a linear problem. Unfortunately, some BFS code show some success in some set of N puzzle problem. may be this sub set is only a linear sub set of all possible permutation. That why for non linear or very special configuration, all path finding algorithm failed. Some one have found or have inferred to the one of the initial configuration as the above. I have tested it in many real code and it stuck going from node to node, the cost fluctuate down then up then down then up and almost never reach goal.
https://algorithmsinsight.wordpress.com/graph-theory-2/implementing-bfs-for-pattern-database/

[おとめ座 ひなたぼっこ]

I have a small suggestion for you.
As I said earlier, when you use any path finding algorithm to traverse the node tree, the adjacent node has smaller taxicab than initial node. But the fact is that all pieces of N-puzzle are correlated. So if you move one piece closer to its correct position to gain better cost, probable you move other piece further its correct position. So instead of just simple re-calculate the cost when you create
a new node. I suggest you make another calculation to ensure all pieces go closer to their corresponding correct position. This way, it will cost you more processing resources but eliminating invaluable node and fluctuation, also ensure 100% success rate on time.

[おとめ座 ひなたぼっこ]

I stop here as if a student in my class cant get any better score.