2

Say that both players collaborate to get White's king to the eighth rank and Black's king to the first. What's the shortest sequence of moves that achieves this?

3

It can be proven that 10 moves, or 20 ply, is the least possible.

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1. f3 f6 2. Kf2 Kf7 3. Kg3 Ke6 4. h3 h6 5. Kh4 Kf5 6. Kh5 Kf4 7. Kg6 Kg3 8. Rh2  Rh7 9. Kxh7 Kxh2 10. Kh8 Kh1

Here is the proof, listed in a logical order.

Observations Of Proof

  1. Both kings must make at least seven moves to get to the other rank, so that's 14 ply off the bat.
  2. Each side must move a pawn move to release a king, which costs 2 ply in further total.
  3. Each side must move a piece to unguard a square for the other king, also costing 2 ply.
  4. Finally, at least one more pawn move by both sides is required in order to let each king bypass the pawn structure, and that amounts to 2 ply.

In conclusion, the add up 14+2+2+2=20 from the proof shows that 20 ply is indeed the minimum possible.

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