The Retrograde Analysis Corner
Glossary
In chess competitions, any side is allowed to claim a draw when the game saw fifty consecutive moves (i.e. 100 single moves) occur without any capture or any pawn move. That is, without any irrevocable progress towards a conclusion. (There are some additional conditions having to do with the organization of chess tournaments.)
In retro-problems, a position is a draw whenever it can be proven that necessarily (i.e. in any proof game) fifty consecutive moves have occurred with no capture, no pawn move, and no castling. (Castling has been forgotten in the FIDE tournament rule :-) The main reference on this theme is [Pla79] (but see also [Pla69]).
T. Volet Ded. M. Caillaud & N. Plaksin 1st Prize Rex Multiplex, 1983
14+12. Draw
Here, the 75 last (double-) moves may not have involved captures or pawn moves (or castlings!)
Let's see: all captures have been done by P's. Taking back any move by a wP from the West side would entomb the bK behind an unbreakable barrier.
Indeed, the only way to unlock the position is to take back b6-b7 so that the bK can be extracted from his South prison. This requires first that we drive the bQB back to c8, and that we extract the wK from the f8-h8 squares. The bKR must be in the North cage when we take back b6-b7. The bQB will be uncaptured by h3xBg4 (with the wKR in its cage), but we first need the Rg1 to help extract the wK.
This rook has a long way to go from g1 to a1-a3-b3-b5-a5 to f8 before it can be used to shield the wK from the bRe7. This trip involves delicate crossings with two Bs and the bK.
When the wR eventually reaches the 8th rank, we can extract the bR from e7, so that the wK himself can wait in e7. Then the bR must switch position with the wR: for this, they both have to go out of the cage, taking the long journey. Then the bR can be reinstalled on the 8th rank with the wR as a shield that will allow the wK to wait on b5. Then at last the wR can go back to h1, allowing h3xBg4 to be undone and the whole mess to unlock.
