Hello,
I don't understand something in a retro analysis problem from the collection of Raymond Smullyan. Here is the chapter:
........ (copyrighted material omitted)
And now my question: why couldn't the pawn on a3 come from d4 with a capture? Because, if I understand correctly, the given position is the one after the White Knight move of Palmerston. we could imagine a game like this, with a White last move with the Knight:
I suppose you meant: why couldn't Pa3 have come from b4 (instead of d4)? Well, congratulations! You just graduated from Smullyans Deductive errors course and may now progress to Post Smullyan inductives. For the appropriate fee of $5000,- that is!
I heard mention of errors in Smullyans work but never noticed one myself. You definitely did. This is the sort of error every retrograde composer makes once and a while when incessantly alternating forward and backward play. That sometimes drives you mad. Smullyan could have picked the bishop or the rook but not the knight as the piece he (Sherlock) witnessed on the move. The most elegant version is probably given in the following, slightly amended, diagram, with this instruction:
............. Sherlock had forgotten his glasses and his vision was blurred when he saw Sir Arthur Palmerston complete a move with a white unit. It was too big for a pawn and also certainly was not a knight, since he would have recognized its graceful skyline even after consumption of a bottle of whisky on top of his eyesight troubles. .................
Hello,
I don't understand something in a retro analysis problem from the collection of Raymond Smullyan. Here is the chapter:
A month later we received another invitation from Sir Reginald. We accepted with pleasure. The gathering was far smaller than on the preceding occasion.
Sir Reginald led us into the library. To our delight, there were the Palmerston brothers, again at a game of chess. Just as we entered, I saw Arthur Palmerston completing a move with a White knight. Then they both saw us and jumped up to greet us. After the usual formalities, we all sat down for a
delightful evening.
"I'm sorry I missed your fantastic demonstration last month," said Sir Reginald. "But, of course, Arthur and Robert have explained it to me down to the last detail Really quite brilliant, Holmes!"
"As a matter of fact," said Holmes with an extremely grave expression, "I was really silly—most silly about the entire thing! When I got home, I suddenly realized that I could have solved the whole mystery far more efficiently than I did! Yes indeed, had I used empirical rather than purely logical methods, I could have solved the problem in a fraction of the time!"
"How?" asked both brothers almost simultaneously.
"Why," said Holmes, with his old merry twinkle, "by opening the box of chess pieces which you gentlemen so trustingly left behind when you went out onto the terrace."
This got a good general laugh. The conversation then turned to the question of whether Holmes, had he used such an unfair method, would have technically won the bet. Sir Reginald maintained that he would not, arguing that the terms of the bet specified that Holmes not only name the piece correctly, but prove it was the right one. Arthur Palmerston maintained that Holmes would have won.
"It all depends on how you define the word 'proof,' " he said. "After all, proofs are of two kinds—deductive and inductive. The word 'deductive' did not enter into the terms of the agreement. If Holmes had opened the box under our very noses," Arthur Palmerston continued, "and shown us the thirty-one pieces lying collectively in the box and on the table, the identity of the missing piece would have been established beyond any reasonable doubt. Surely, any natural philosopher present would have qualified this as a 'proof.' ''
Well, here indeed was an amusing puzzle! The conversation then got deeper into semantics and the philosophy of inductive evidence. Holmes, meanwhile, had been looking with increasing interest at the Palmerstons' suspended game. Presently he took out of his pocket a notebook, tore off a piece of paper, wrote something on one side, folded it with the writing inside, then wrote something on one of the half-sides, folded it again with the new writing inside, and placed the folded note on one side of the chess table—not on the squares, but on the margin. This was the position:
"You know," said Holmes, "I would like to see this game concluded. It possesses some interesting features."
"By all means," said Sir Reginald. "Why don't you continue it? I would be delighted to watch!"
The two brothers went back to their original seats at the chess table. It was about a minute before either moved. Then Robert Palmerston put his left hand on the king and his right hand on the rook and was about to castle. Arthur raised his head and was about to say something when Holmes sprang up like a tiger and said, "No, no, Mr. Palmerston! Before you move, will you please half-unfold this slip of paper and read aloud what I have written?"
Robert picked it up and read aloud, " 'You can't castle! You really can't, you know!' "
I don't think I have ever in my life seen a man look more surprised! "Good God, Holmes," he exclaimed, "this is really too much! This is indeed a double mystery!"
"Well," said Holmes, laughing, "if you will completely unfold it and read the rest, I think one of the two mysteries will be cleared up."
Robert Palmerston did so, and read, " 'While I have been studying this intriguing position, Robert Palmerston has been studying me. I think he knows I am on the trail! I predict that when he goes back to the game, he will pretend to castle, just to test me!' "
"Capital joke!" roared Sir Reginald. "Really capital! And now," he added more seriously, "would you be so good as to explain to us the other mystery? How did you know he can't castle? Were your methods deductive or inductive?"
"Oh, purely deductive," laughed Holmes. "Except for the fact that I did see White's last move as I entered the library. Were you aware of that, Mr. Palmerston?"
"Why, certainly," replied the younger Palmerston. "If you hadn't known White's last move, then you couldn't have known that I can't castle."
"Correct," replied Holmes. "Only how did you know that?" Holmes inquired as he turned to Robert Palmerston.
"Oh, Holmes," was the answer, "this last month I, too, have learned a little about retrograde analysis."
"Splendid!" replied Holmes. "Really splendid! In that case, then, you probably already know my analysis?"
"I believe so," said Robert, "only I would like to hear it from your own lips to see how it tallies with mine."
"Splendid," replied Holmes once more. "Now then, we first observe that the White pawns have clearly captured all six missing Black pieces—the one on a5 has captured two, the one on g3 has captured one, and the one on h5 has captured three. Now, White's last move was not with a pawn (since it was with a knight), hence it did not involve a capture. Therefore, immediately before White's last move, there were no other Black pieces on the board."
"Clear enough," I remarked.
"So then," continued Holmes, "what was Black's last move? If it was with the king or rook, then of course Black can't castle. If neither the king nor the rook moved last, then the last move was made by one of three pawns on a3, e5, and g6. Now, e5 did not move last."
"Why not?" inquired Sir Reginald.
"For the following reasons: The Black pawn on a3 has made at least three captures, if it came from d7; it has made four, if from e7. The pawn on g6 has made one capture. This accounts for at least four of White's five missing pieces. Thus the pawn on e5 did not make two captures."
"I'm with you, so far," said Sir Reginald.
"Well then, this means that e5 did not just come from f6, or else it would previously have had to come from e7, making two captures."
"Right," I said.
"On the other hand, it could not have just come from d6, or else either it came previously from e7—again making two captures—or else it came from d7, in which case a3 must nave come from e7 rather than d7, and this would collectively involve six captures, including the capture on g6, which is one too many."
"Good," said Robert Palmerston.
"Therefore," continued Holmes, "if e5 moved last, it must have been from e6 or e7. It couldn't have come from e6 or it would have been checking the White king. And it couldn't have come from e7 as then the Black bishop from f8 could never have got out on the board to be captured by a
White pawn."
"Capital!" said Sir Reginald.
"Now then," continued Holmes, "we know that e5 did not move last. Hence—still assuming that neither the Black king nor rook moved last—the last move was made with one of the pawns on g6 or a3. And now I will prove to you that in either case, the Black king must have moved sometime earlier in the game—though in each case for quite a different reason! Well, suppose g6 moved last from f7. Then the Black king must have moved sometime earlier to let the Black king's rook out onto the board to be captured by a White pawn."
"Clever," I remarked.
"That is the easy case, Watson! Well now, suppose a3 moved last. It must have been from a4. Now comes the remarkable part! Since a3 was just at a4, it must have come ultimately from d7, making its three captures on c6, b5, and a4, which are all white squares. And the pawn on g6 has captured on a white square. Thus four of the five missing White pieces have been captured on white squares. Now,
the White queen's bishop originally from c1 fell on a black square, so was not captured by the pawn either on a3 or g6.
Therefore the four pieces captured by those two pawns include the White pawn originally from d2. This raises a little problem! For this pawn to get captured by the pawn on a3 or the pawn on g6, it would have to have left the d-file, but how could it, since all six missing Black pieces have been captured by a5, g3, and h5? The only possibility is that the pawn from d2 has promoted! So, if the pawn on a3 moved last, then the pawn from d2 promoted. It must have come straight down the d-file, and when it came to d7, the Black king had to move out of check—unless, of course, it had already moved away. Therefore, again Black can't castle.
"To summarize, gentlemen, either the Black king or Black rook has moved last, in which case Black can't castle, or g3 has moved last, in which case the Black king has previously moved to let out the other Black rook, or a3 has moved last, in which case the Black king has previously moved because of the promoting pawn from d2. Which of the three possibilities is the actual one cannot be analyzed—only the players themselves can know that. But in none of these instances can Black castle."
And now my question: why couldn't the pawn on a3 come from d4 (edit: b4) with a capture? Because, if I understand correctly, the given position is the one after the White Knight move of Palmerston. we could imagine a game like this, with a White last move with the Knight: