Capablanca's Last Lectures: Felix Culpa!
The conjunction of the White king on g3 with the two pawns on g4 and g5 tells any reasonably experienced solver that the solution will be a stalemate (what else is the function of the pawn on g5?), and the most obvious construction will involve the Black queen on d1 and the Black king on g1.
So, my first thought went like this:
1.Re5+ Kf1 2.Rf5+ Kg1 3.Nb3 cxb3 4.Rd5 a1(Q) 5.Rd1+! Qxd1 stalemate, but even as I thought about it I immediately realized that 4...a1(Q) wasn't forced at all. Indeed, both 4...Kf1 and even 4...a1(R) seem to win.
My next idea was to see if I could use the knight to some other end, either to create threats on the Black king, force some sort of perpetual, fork, domination or other standard trick, but couldn't find anything useful.
Back to the old drawing board, and time to take a look at the other line-clearing idea: 1.Nd3+ cxd3 (everything else is losing or barely drawing for Black) and now, everything fell into place: 2.Re5+! (a well-known idea from rook vs. pawn endings: either the king blocks the pawn, which slows down its queening, or the king is forced to go further from the pawn, eventually having to waste a tempo returning to a sufficiently near file to defend the pawn from subsequent attack. The former idea counts here, but the latter - the drive-the-king-away-motif - has a different function in this problem) Kf1 3.Rf5+! Kg1 4.Ra5 d2 5.Rxa2 d1(Q) 6.Rg2+ Kh1 7.Rh2+ Kg1 8.Rg2+ Kf1 and now the punchline: 9.Rg1+! Kxg1 (9...Ke2 10.Rxd1 Kxd1 11.Kxg4 and 12.Kxg5) stalemate!
Not a masterpiece, but a nice puzzle: the drawing mechanism was obvious, but the false lead, the 2.Re5+ 3.Rf5+ finesse and the second rank checking idea offered a significant improvement over the banal variation of my first try. Problem solved, and after double-checking my analysis, I consulted with Capa: did I miss anything?
Imagine my shock: Capablanca completely missed my main variation, gave the false lead as the solution and didn't consider anything on move 4 except the cooperative 4...d1(Q)! We're talking about one of the greatest players of all time, so of course I double-checked everything yet again, but I was right and Capa wrong.
Needless to say, there are many morals. Here are three:
1. Even GMs make mistakes!
2. We're all fallible, but if you're done your best, then trust your judgment. Sometimes, it may even be better than a world champion's.
3. The brilliance of even the greatest minds is no match for the deleterious effects of sloth. Capablanca's unwillingness to be self-critical and work hard when he reached the top probably cost him his title against Alekhine (a view shared by, among others, Alekhine himself, Mark Dvoretsky and Garry Kasparov), and even in this trivial case, his unwillingness to take a second look at the puzzle caused him to miss a fairly simple rejoinder - and to miss out on the full aesthetic value of the study as well!