An introduction to composed chess problems

First, you should learn what a basic term like "cook" means in chess problems. A cook is a solution unintended by the composer, regardless of the number of solutions that work. An unintended solution doesn't magically become intended just because the intended one fails to work.

Cook: A second key move, unintended by the composer. A cook is a serious flaw, and invalidates a problem. The publication of cooked problems was once common, but in the modern era computers can be used to check for cooks, and cooked problems are rarely published.

https://en.wikipedia.org/wiki/Glossary_of_chess_problems#C

If the key fails to work, that also invalidates a problem. When such a problem is cooked as well, that makes the problem doubly faulty, which may be unusually bad, but not extraordinarily good. This was Reti's first problem composed as a child, made before computer-testing was possible, so no offence to the great man. 

You are confusing "subjective" with arbitrary. I gave sensible, non-arbitrary reasons for why 1.Qh8! is better and more beautiful than 1.Qf2+, based on established chess problem aesthetics. But you are unable to provide a single reason for why you think something that's "straightforward" is more beautiful. Instead all you have is "it's all subjective anyway". That means you could pick any of your games where you won after a blunder by the other side, and claim it's more beautiful than Fischer's Game of the Century, because your game is more "straightforward". And when asked to justify this claim, you say, "it's all subjective anyway". Hmm, right.

You can find the story of Reti's first problem here which further quotes a source explaining the intended key and cook. Here's a google translation of the relevant part:

The intended solution 1.Dh8! with the threat 2.Dxe5 + Kxc4 3.La2 dull 1 ... Dxh8 / Sd7 / Sg6 2.Kb4! De5 3.c3 # does not work because of 1 ... Kxc4 2.Qxe5 b5 + 3.Ka5 f2 4.Ne3 #, which neither Gottschall nor the readers noticed. On the other hand there is another solution, which certainly would not have been in the sense of the young inventor: 1.Df2 + Kc3 Or 1 ... Kxc4 2.La2 + Kc3 3.Lxe5 # or 1 ... De3 2.Dxe3 + Kxc4 3. La2 #. 2.Lxe5 + Kxc4 3.La2 #.

In a Draw endgame study, if a win is possible then it's cooked (since best play by White is assumed). If a problem requires you to find a M2 exactly when M1 is possible, the "exactly" part of the task must be given as part of the stipulation to warn the solver, otherwise the problem is unsound. 

The sources I linked to above suggest that the problem was really unsound when first published rather than misprinted. But I've computer-tested your correction and it's sound. So well done in fixing this problem so neatly!

So no known exceptions! This assumed white's best play concerned me, as the solver would be somehow warned with the stipulation by the title "white to play and draw" instead of "win"... ty!

Btw great reference-links on your #21 about Reti

@introuble2 Yes, the task of a problem or study should always be given with the position. When it's not provided, as is the case with the Daily Puzzles on this site, that causes a lot of unnecessary confusion for the solvers (as seen in many frustrated comments in the Daily Puzzles threads from people not familiar with studies).   

@Rocky64

Again, and hopefully the last time.

Cook is defined as the second (third, etc.) key move unintended by the composer. More important is "the second" than "unintended". So, the first (intended) key must exist. If it doesn't exist (because if it doesn't work, it is not the key), the unintended key is the only and main key. Chess problem is cooked, only if there are 2 or more working keys (no matter if intended key is one of them or not).

Direct mate classic chess problem is supposed to have exactly 1 working key, and Reti's problem has exactly 1 working key. Therefore, Reti's problem is 100% correct. From the pure solver's point of view, your task is to find the correct working key, you aren't supposed to know what was intended. You can only guess, based on conventions and your (subjective) aesthetic feelings.

I gave it as example, where the supposed "cook" became the key, since the intended key doesn't work. Reti gave no comments about 1. Qf2+!. What if he knew the secret and just made the fun at the expense of aesthetic problemists? If I had his composing skills and computers weren't around, I certainly would.

@Polar_Bear A computer would solve Reti's problem and find the single 1.Qf2+ solution, and that's it. It's incapable of understanding that 1.Qf2+ is actually a cook and the intention was 1.Qh8. And of course it has no idea that 1.Qh8 would've been the more artistic key. You are taking the computer's limited perspective and ignoring the intentional aspect of words like "cook" and "key", just as you were ignoring established chess problem aesthetics by claiming that 1.Qf2+ is more beautiful than 1.Qh8. However, reality is not determined by a limited perspective, even if yours - unlike the computer's - is based on wilfully ignoring the existence of those things.

@Rocky64

It seems to me you still consider 1. Qh8 as a key, when it is not. Because it doesn't work! Therefore, the true key 1. Qf2+! cannot be a cook, because there is no other key. Understand?

Look at it from the solver's perspective. You know no intentions, just stipulation, you find 1. Qf2+ and that is it. Maybe you also discover the try 1. Qh8 and think "... it was composed by some puzzler-patzer, but if the white king was on a3 instead, then Qh8 worked and Qf2+ not, damn, it would be a decent puzzle."

We know nothing about Reti's intentions. Maybe he liked it as it is: artistic try Qh8 vs the brutal key Qf2+.

And yes, I like the 1. Qf2+! exactly for its unsubtle brutality, especially the line 1. ... Kxc4 2. Ba2+ Kc3 3. Bxe5#. How decisive: white captures the queen with checkmate. That way it frequently ends in real games, when mating attack occurs and defending side doesn't resign. It is nice.

I understand your computer-like perspective - conflating "key" and "cook" because intention is too hard to handle and must be ignored - very well, because I use computers all the time.

It's easy to work out Reti's intention - just read the published solution, a scan of which is shown in the article I linked - and it says 1.Qh8. Even you realised it at the beginning in post #15 when you wrote, "The intended solution was 1. Qh8". 

Please don't project your misunderstanding of composed chess problems to the great Reti.

 And yes, I like the 1. Qf2+! exactly for its unsubtle brutality...

As already mentioned, no one can tell you what you like. But if you suggest that such a banal cook is artistically superior to Reti's intended solution, expect to be corrected.

@Rocky64

I think you are still missing the true essence of Reti's puzzle. It is that two unintended (?) flaws eliminate one another, together making the puzzle correct. From this point of view, the puzzle is sort of unique and I find it excellent. The "mundane" post-key play with "artistic" virtual play together create specific and funny trap.

Many people "found" Qh8 and missed Qf2+, because they followed conventions and didn't analyze checking moves properly. You may not like the "banal" Qf2+, but it is actually harder to find than Qh8 for experienced solving problemists, because they don't expect check as the key move.

Yes, it's ironic that a double-flaw results in a problem with a single solution and that's unusual, though in the pre-computer age there were so many cooked problems that it's not surprising a few would also have a failed key. And you're right in that if Reti's problem were used in a solving competition, some expert solvers could miss the solution because it starts with a check. Such "trickery" is a different issue from the quality of a problem. If 1.Qf2+ were the intended solution, the problem wouldn't have been published in the first place.

In directmate problems like Reti's, cooks are generally of no artistic interest, but in helpmates there are rare cases where an accidental solution is of such good quality that it gets incorporated as part of the problem's official solution. The best-known instance of such remarkable luck was a very early helpmate by Sam Loyd. 

Is it possible that Stockfish would have trouble solving a simple-looking Mate-in-2 problem like this?

Ditto.

More folks who like talking more than singing. 

No.

Btw, is the diagram correct? There is missing somethig, I guess. The position seems illegal to me: What was the last black's move?

You noticed something unusual about the position (which is actually legal) - something that Stockfish is incapable of seeing. So unlike the engine, you are close to solving this problem!

If it's white's turn seems illegal to me too. If it's black's turn seems legal and it's again mate in 2 white's plies. 1... Kxa7 forced 2. c8=R Ka6 forced 3. Ra8#

So you claim, if you input black-to-move in the position above into Stockfish, engine can't find the mate-in-2 after the forced 1. ... Kxa7. Really? Nope, engine finds it immediately.

Well, I think the issue with solving engines is that you must give them full hard information. Engine will not guess which side to move (+ castling and en-passant rights) from legality check or retrograde analysis.

The point of the problem is that Black has no possible last move, which means the only way the position could have arisen is that White made the last move. So it's Black to play, and as introuble2 mentioned, the solution is ...Kxa7 1.c8(R)! Stockfish (or any engine) is of course incapable of doing this sort of deduction or retrograde analysis, and that's why it can't solve this mate-in-2.

The alternative way the position could have arisen is that Mr. Knud Hannemann composed it and the diagram shows starting position of specific chess variant. Chess960 starting positions are illegal as well, aren't they?

Stockfish finds checkmate quickly in both cases, white or black to move. You must, however, enter which side to move, and you can't argue, if you set white, that 1. c8=Q+ Kxa7 2. Qb7# is incorrect solution.

To be honest, I am quite disappointed. Everytime somebody posts a puzzle "computers can't solve this", it is almost always some sort of joke: en-passant, castling, chessboard from the black side without a notice (ie. pawns go backwards), or defending side to move also without a notice. Very rarely somobody posts a puzzle which works a bit, and it exploits the known weak spot of engines: null-move-algorithm failure in zugzwang. There must be, however, enough material on the board, or the null-move-algorithm is turned off.