Black to move, why is Qa7+ the only winning move?

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Wh0aMama
Can someone explain the solution of this puzzle to me. I think I'm missing a broad idea that perhaps makes solving this easier than brute forcing the calculation of multiple lines. Correct move is Qa7+, what themes should I be aware of to be able to find this. 
 
It is worth noting, database has four moves winning for black in this position: Qa7+ (the solution), Qf1, Qh1+, and Qa8, but after white replies with Kg7 against all lines except the solution, the only winning move becomes going back to Qa1 with the idea to play Qa7+ once again. Letting Stockfish 12 sit on this position until depth 30ish, confirms that Qa7+ is the only winning move here. 
 
Any help analyzing this would be appreciated. 
 

 

Martin_Stahl
Wh0aMama wrote:
Can someone explain the solution of this puzzle to me. I think I'm missing a broad idea that perhaps makes solving this easier than brute forcing the calculation of multiple lines. Correct move is Qa7+, what themes should I be aware of to be able to find this. 
 
It is worth noting, database has four moves winning for black in this position: Qa7+ (the solution), Qf1, Qh1+, and Qa8, but after white replies with Kg7 against all lines except the solution, the only winning move becomes going back to Qa1 with the idea to play Qa7+ once again. Letting Stockfish 12 sit on this position until depth 30ish, confirms that Qa7+ is the only winning move here. 
 
Any help analyzing this would be appreciated. 
 

 

 

Do you have this set up correctly? This is a straight draw according to analysis, not winning.

 

edit: Nevermind, the game insert is set as white to move

Martin_Stahl

It's basically that the other solutions, end up with the transposing to similar lines but take extra moves to get to that position.