Synchronised swimming

8/1R2p3/2pkp2N/2p1p3/2p5/2P5/8/7K w - - 0 1
White to move and mate in 10 moves
Renato Di Vincenzi, 1998

“Both sides interact like synchronised swimming in this rather queer set-up for a problem! Can you crack the code? 😊”, the editorial staff of ChessBase India wonders... Maybe yes: 1. Kg2 Kd5 2. Kf3 e4+ 3. Kf4 e5+ 4. Kf5 e6+ 5. Kg4 e3 6. Kf3 e4+ 7. Kf4 e5+ 8. Kf5 Kd6 9. Nf7+ Kd5 10. Rd7# 1 : 0.