Two corrections are involved in the following very famous study. Its complete history, including how it was adapted from the conclusion of a game, are beyond the scope of this answer, but may be read on web pages from Wikipedia and the archive of Tim Krabbé's Open Chess Diary. When first published in study form, it was a draw-study as follows:
[Title "G.E. Barbier. Glasgow Weekly Citizen, 4 May 1895. Black to play and draw."]
[StartFlipped "0"]
[fen "8/2P5/1K6/3r4/8/8/8/k7 b - - 0 0"]
1... Rd6+ 2. Kb5 Rd5+ 3. Kb4 Rd4+ 4. Kb3 Rd3+ 5. Kc2 Rd4! 6. c8=Q Rc4+ 7. Qxc4 =
Rev. Saavedra read the above solution, given by Barbier the following week. He then cooked Barbier's draw-study, showing how White could force a win:
[Title "G.E. Barbier, corr. Rev. Saavedra. Glasgow Weekly Citizen, 18 May 1895. Black to play and White to win."]
[StartFlipped "0"]
[fen "8/2P5/1K6/3r4/8/8/8/k7 b - - 0 0"]
1... Rd6+ 2. Kb5 Rd5+ 3. Kb4 Rd4+ 4. Kb3 Rd3+ 5. Kc2 Rd4! 6. c8=R Ra4 7. Kb3 {and wins}
(The study is usually given in the version by Lasker; White's pawn is moved to c6, the stipulation is changed to "White to play and win", and there is an extra move 1. c7.)
Saavedra's move is beautiful in being a rook-promotion which, in a position with only four units, is the only winning move. And he transformed a draw-study into a win-study which is beautiful in that it puts White in that position and forces that promotion.
Except ... it doesn't. Tablebases have shown that White can indeed force a win, but Black avoids the Saavedra position, and White can win only by promoting to queen. At move 3, Black's best defence is not 3. ... Rd4+
but 3. ... Kb2
(deferring mate for 3 more moves) giving White only one winning move: 4. c8=Q!
. If Black does play 3. ... Rd4+
then White's best attack, supposing that Black always plays the best defence, is either 4. Kb3 Rd3 5. Kc2! Rf3 6. c8=Q!
or 4. Kc3 Rd1 5. Kc2 Rf1 6. c8=Q!
.