Extract from Noam Elkies' Article in EG 143 magazine, Jan 2002

We have no Unoriginals this time, but our final Original is rather heterodox. Its author, Andrew Buchanan, is the inventor of "Dead Reckoning", which hinges on the FIDE rules for "dead positions" (see Andrew's recent articles in the Problemist and StrateGems, or his tutorial [here]).

More recently Andrew noticed a similar opportunity in the Codex treatment of the 50-move rule. This rule is generally ignored by composers, who recognize it as an arbitrary and imperfect approximation to the idea that the game is drawn if neither side can make progress. But there is a genre of remarkable positions that can be retroanalytically proved to have reached or be on the verge of reaching the 50-move limit. The Codex recognizes this by stating: "Unless expressly stipulated, the 50 moves rule does not apply to the solution of chess compositions except for retro-problems." What Andrew discovered was an unintended consequence of this convention.

[Diagram {C} appears, with the additional notation: "[a4a2 0332.00 a1b1b2d3 3/3=, I think]"]

Generically Black's material advantage is winning (L.Stiller), but here White has counterplay.  Is it enough?

a) By default the stipulation means "White to move and Draw", which is done by 1. Kb4! Bc2 2. Kc3! simplifying to a 0301 draw, e.g. 2... Bb3 3. Nb4+ or Nc4. According to Thompson's online database, White's first two moves are unique; White has several inferior alternatives on move 2 or 3, such as 2. Kc4?, that lose in some 200 moves, but the fact that this is well beyond the 50-move limit is irrelevant.

b) A familiar paradox: despite appearances, this is not equivalent with (b), since Black has no last move (0... c×b1=B works only on White's side of the board). So it is Black's turn, and 1... Bf7+ disentangles and wins. But now the new twist: since we have invoked retroanalysis, this is a "retro-problem", and White still draws starting 2. Kg5! Kg8! 3. Kf5(f6)! as long as he can hold Black at bay for at least 50 moves.

Several more examples can be found [here]. Andrew's [{A}] is the only example so far with no captures before the 50-move span. It is also the only one with a 180-degree twin, which raises a further conundrum: to check that White may move in (a), we must find the unusual 0...c×b1=B; doesn't that make (a), too, a retro-problem, to which the 50-move rule applies?...

[AB: Thank you, Noam. His final point is interesting. See the discussion on what is a retro-problem in the solutions page. I consider (a) is definitely not a retro-problem. By default we assume that a position is legal, unless we can prove otherwise. The fact that there is just a single legal last move in this position, and it is perhaps a bit "quirky", is is not part of the solution.]

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