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Janis Betins - Mate in 6 - Latvis, 1927

A lucid more-mover that shows a popular thematic combination. It's White to play and mate in 6. What is the key move?
1. Rf1 g3 - How does White continue?
2. Nf5 Kg2 - White to play. Keep going.
3. Ne3+ Kh1 - And now comes the thematic move of the solution. What would you play here as White?
4. Rc1 g2 - White to play. Keep going.
5. Nd1 Ne2 - Final move. White to deliver the coup de grace!