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https://chesspuzzle.net/Puzzle/37161

[FEN "r4rk1/2p2n1q/1p1b4/3Pp3/2Q2pP1/P1N1B2P/1P4P1/2RR2K1 w - - 0 1"]

1. Ne4 

The answer given is Ne4, which is followed by the pawn on f4 capturing the bishop on e3, at which point white is able to fork black's king and queen, however this is entirely avoidable by black simply moving either the king or queen to a square that prevents the fork from happening, e.g. Qh6. So why is Ne4 a better solution to this puzzle than simply moving the bishop to a safe square, e.g. d2?

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You're absolutely right. Black can avoid the King + Queen fork by playing Qh6 instead of fxe3. But the reason why Ne4 is better than Bd2 is because it centralises the knight and prevents Black from bringing their Knight to g5. What does Ng5 do? First, Black threatens to sac the knight on h3 for two/three pawns and weaken the white king. Second, it prevents white from going to Ne4.

Having a knight on e4 definitely gives white an upper edge over black and makes it difficult for Black to create plans.

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