White to move. Black is attacking both the g2 and g4 pawn. The White King has no way of defending either Pawn. Is White’s position hopeless? Should White resign? 
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No Nd5+ king moves then Ne3
Bonjour Susan,
1. Nd5+ – King move’s
2. Ne3 – King move’s
3. Kd4! and
4. Kd3 and
5. Ke2 and
6. Kf2 1-0
Au revoir !
Nd5+ and Wht wins 1 Nd5+ Kf7 Ne3 forces Blk to trade R for N and Wht is up 3 pawns to 1.
TFK
To clarify fenchplayer’s excellent solution, the third move is critical to gain a tempo. Other attempts seem to lead to a draw at best. For example, if
1. Nd5+ Kf7
2. Ne3 Kf6
3. Kd3?! Ke5
4. f6 Forced? If 4. Ke2 Ke4 and Black would win after 5. f6 Rxe3+ 6. K moves Ra3 7. f7 Ra8. Or if 4. Kd2 Ke4 5. f6 Rxe3 6. f7 Rd3+ 7. K moves Rd8.
4. f6 Kxf6 5. Ke2 Ke5 6. Kf2 Ke4! 7. Kxg3 Kxe3 looks like a draw.
But 3. Kd4! avoids all that and forces Black to retreat the King, losing a critical tempo. 3. … Kf7 4. Kd3 Kf6 5. Ke2 Ke5 6. Kf2 and wins.
frenchplayer
nice solution. pretty clever.