Dead reckoning puzzles

Dead reckoning puzzles are where you have to work out the move made last based on this rule: the game is drawn when a position has arisen in which neither player cna checkmate the opponent's king with any series of legal moves. The game is said to end in a 'dead position. Here is an example.

In this position, if black moved last, he would have had to take a piece on a8 because otherwise the game would have been drawn earlier. If it was a knight or bishop, then neither player could checkmate so it would have been a draw earlier. If it is a queen or rook, black would have had to take it, so it would have been a draw earlier. Therefore, white moved last and we can even establish what move he made: Kxc6.

cool

But the position after 1.Ra8+ is already dead, so Black could not have played 1...Kxa8.

Yes, after 1.Ra8+, black is forced to take(it is the only legal move), making a dead position before the capture.

By the way, in the puzzle above, white is to play (so black moved last) so the answer cannot be fxg4. Also, I said it was not too hard. That is wrong: it is quite hard.

I will give you a hint: the position is dead, but only in this specific position. How can white checkmate in a slightly different position?

Obviously black's last move cannot have been with the king if the position is alive, so black's last move was ...a5-a4. It remains to prove that that position is alive.

Retract -1...a5-a4. From that position, a mate is:

1...Ke8 2. Ka6 Kd8 3. Bb7 Ke8 4. Bc8 Kd8 5. Kb7 Ke8 6. Ka8 Kd8 7. Ba6! Ke8 8. Bb7! Kd8 9. Bc8! Ke8 10. Bd7+ Kd8 11. Be8 Kc8 12. Bf7 Kd8 13. Bg8 Ke8 14. Kb7 Kd8 15. g5! Ke8 16. Kc8 a4! 17. Bf7#.

Moves 7-9 are to allow the bishop the right timing to pass the black king. Move 15 wastes a white tempo, while preserving black's extra tempo ...a4! on the next move.

Well done, Remellion!

That you, Andrew? :)

There are some highly capable solvers here. Remellion, caveatcanis, chaotic_iak, shoopi, etc.

Here's another to satisfy your lustre for puzzles.

White can castle; -1...Kh1xR -2. Rg2 Kg1(x~) -3. Rf2x~ and the position unwinds, with a promoted wR. -2. Rg2 must be without capture.

Alternative game history is -1...Kh1 -2. g2, promoted wB and white cannot castle.

If white cannot castle, the position is dead (inevitable stalemate).

If the last move was -1...Kh1 w/o capture, the position before that move is also dead and the game would have stopped there.

So it had to be -1...Kh1xR.

Seems like I still don't fully get this DR stuff, then...

The second problem is cooked by : -1. (...) Ke8xNd8 (position is not dead). For instance, the last two moves could have been : Nh8-f7+, Kd8-e8, Nf7-d8, Ke8xd8 (draw by dead reckoning).

Not quite true.  Given your last move, the position was dead before black played it. What else could he have played than ... Kxd8 that might still possibly lead to a checkmate?

Note that black has no tempo move in this variation unlike the main line where he retracts ...Pa5-a4.

Reproduction of comment #7:

I can now announce with great certainty that this is a silly puzzle as of 2015. Much sillier than the one I posted 2 days ago (https://www.chess.com/forum/view/more-puzzles/mate-in-two-634) on this forum. It is because the Codex conventions changed in 2015 to state that the dead (reckoning) rule does not apply to compositions, except when they are retro-problems.

There is however nothing to suggest that this is a retro-problem because it is easily retractable and fully (though silly) solvable by the simple moves 1. g5! Ke8 2. Kc8= which was intended as a try by the composer. Only when you start from the assumption that it is a retro-problem then the dead reckoning retro content will start to appear. In other words, the new Codex convention is activated through a circular logical condition which is the very definition of sillyness!

This is one of the things wrong with the 2 new Codex articles which depend on the condition "except for retro-problems". In the absence of an objective definition for "retro-problems" these articles tend to be abused in a circular fashion as exemplified by this problem. The difference with my problem is, that it uses a distinct retro attribute to establish its retro-identity and thus avoids circularity of deadness.

There is hope to salvage problems like this one but it needs precisely the mechanism which the designers of the current Codex are trying to get rid of at all cost. It's context. Make sure that every solver knows by context that the diagram is a retro-problem before he commences tackling its solution! And there is more hope. Both the FIDE dead rule and the Codex convention are non-optimal and could be improved upon as I will suggest in an upcoming post. We will no longer need a retro-condition on this problem-type. In this theater, soon!

[Disclaimer: obviously I have assumed the puzzle was posted as originally published]