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The Mighty Gajah

I have tried many possible moves myself and been analyzing with stockfish 6 and houdini 4 engines for more than 2 hours and still no indication that white can win this unless black plays inaccurately. I would love to be proven wrong but I just don't think there is a win for white here.
"They can't concentrate, they don't have stamina, and they aren't creative. They are all fish"
the mighty Bobby Fischer.
what I like about this is one is that unlike other studies or puzzles ,doesn't require deep calculation , u have to be imaginative and thinking out the box to find they KEY for the solution
Okay, a few little hints, and please discard your engines for this, they're no good. SF 6, Houdini - nothing figures this out until you play the right moves and it finally 'gets' it.

Figure out what each and every single piece is for, it's an intentionally well-crafted endgame study.

Zugzwang.
And yes, white does indeed win in twelve moves with perfect play from black.
Wow. This is truly amazing. Thank you AdmiralA for the hint. I was about to give up and forget about this puzzle.

Engines can't find the solution because they can't find the key move which probably because doesn't appear rational at first and they focus on one line that leads to a draw position.

Thanks SSSSSSSSSSSSSSSSSSSS for the puzzle :)
Got it after many hints. There are quite a number of plausible solutions, mate in the 11th, 12th and 13th move. The crucial move is the 4th move, provided the previous moves are correct.
it's mate in 12 with perfect black play, no less. the crucial moves are 1,4 and u can consider move 10 if black defends with the night finally

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