Planteamiento del problema

A week later we had a return visit from Sir Reginald, ac- companied by the Palmerston brothers. The visit was not unexpected; Holmes had already set up a chess position in anticipation of it. We were sitting by the fire awaiting their arrival, and Holmes was grinning from ear to ear.

"Why so like the proverbial Cheshire cat?" I inquired. "Oh, Watson," replied Holmes, breaking into a laugh, "I have a little return jest for Sir Reginald, and I just cannot wait to see his reaction!"

We did not, indeed, have long to wait; almost at that very moment Mrs. Hudson showed in our three visitors.

"Well, well, Holmes, what is this?" inquired Sir Regi- nald, advancing towards the chessboard Holmes had set up. "Why, Sir Reginald, this is a little problem composed en- tirely in your honour! The problem is for White to play and mate in one move."

A R ET U R N VISIT

"Remarkable," said Sir Reginald, before he studied the position seriously. "I had no idea that a one-mover could present any challenge!"

Then Sir Reginald turned all his concentration on the problem. After a while he shook his head and said, "I am afraid you've beaten me, Holmes. I really can't get it! The only way White can even check Black is with the knight on g4 either moving to h6 or capturing the knight on f6. But neither is a mate!"

"Are you sure of that?" asked Holmes.

"Why of course!" replied Sir Reginald. "In the first case Black can move to h8; in the second, Black can take back the knight with a pawn."

"No, he can't," laughed Holmes, "because Black is going in the other direction! If your side were really White—as it appears—then how could the White king and queen ever have changed places?"*

"Touché!" said Sir Reginald with a laugh. "You really fooled me with that one! ... And now, Mr. Holmes," he went on, "I hope you will give me a chance to restore my honour! This little problem gives me an idea which, I think, might stump you."

"Excellent," said Holmes, who was clearly in the mood for a challenge.

"One thing, though," continued Sir Reginald. "The idea occurred to me only just now, and I have not yet had time to work out the details. I will have to do this experimentally at the board, but I'm afraid that if you see me moving the pieces about, it may give you too good a clue."

"In that case," replied Holmes, "I suggest that the other gentlemen and I retire to the opposite side of the room for a bit, and let you have the board quite to yourself."

"Excellent," replied Sir Reginald, "but no peeking, you know!"

* The idea for this problem came from a similar puzzle by Sam Loyd in The American Puzzlist.

A RE T U R N VISIT

"No peeking," promised Holmes with a laugh, as we walked across the room.

We sat and chatted pleasantly, and Holmes, true to his word, never glanced in Sir Reginald's direction. I, however, had made no such promise, and I surreptitiously looked over from time to time. But these peeks, I'm afraid, gave me no clues; perhaps I peeked at the wrong times!

About ten minutes later, Sir Reginald called out, "All right, Mr. Holmes, I have it! Pray be seated. The problem again is for White to mate in one."

Holmes studied the position. After a while he said, "I'm afraid you've beaten me this time, Sir Reginald! I really can't see the trick! Had you not shown me this problem im- mediately after the last, I would have guessed it was again a matter of direction. But even if it were a matter of direction, what help would it be? Regardless of the direction, there is no mate in one!"

Wrong!" said Sir Reginald triumphantly. Wrong?" asked Holmes. "Then would you please tell me what is the mate if my side is White, and what is the mate if your side is White?"

Neither side happens to be White," laughed Sir Regi- nald, "as should be evident by the fact that as the board is now oriented towards us, the lower-right-hand corner is a

A R ET U R N V ISIT

black square, instead of a white square as it should be. If you set it right, you will see that there is indeed a mate in either of the other two directions. With White at the right, the pawn on what is now b6 can take the rook on a5 and pro- mote to a bishop or a queen, thus mating the Black king. With White at the left, the pawn on what is now c2 has simply to move to d2 to effect the same thing."

"Rascally!" said Holmes, truly amused. "So that's the real reason you wanted the board to yourself—so you could secretly rotate it ninety degrees!"

"Precisely," replied Sir Reginald.

"Well, Sir Reginald, when it comes to chess jokes, I ac- knowledge you the undisputed master."

The remainder of the evening we spent studying two seri- ous retrograde problems, from which I learned a great deal—as will the reader, if he studies these analyses with care. Both problems were presented by Holmes.

"Here," said Holmes, "is a position in which it can be proved that White can't castle. The proof is rather simple, but I believe the reason why White can't castle will surprise you!"

A R ET U R N V ISIT

The reason did indeed surprise us! White is missing only a rook; Black is missing two rooks and a bishop, which was captured on its own square, f8. Therefore the pawn on b4 captured a Black rook and the pawn on g5 captured a White rook. Black must have captured first, since prior to the cap- ture neither of the Black rooks could have got out on the board to be captured by the White pawn. How then did the missing White rook get out on the board to be captured by the Black pawn prior to the White pawn on b4 capturing? The only possible answer is that the rook on h1 must really be the queen's rook! The sequence was this: First the king's rook got out and was captured by the Black pawn, letting out a Black rook to be captured by the White pawn. Then the rook from a1 came round to h1. So the rook on h1 is really from a1! Thus of course White cannot castle.

"That's a pretty problem," said Arthur Palmerston. "I wonder, if the White bishop were removed from c1, would that affect the answer?"

"Let us see now," replied Holmes. "That's a nice ques- tion, Palmerston! It would make no difference as regards the final outcome, but the proof would be a bit different. In this case, the rook on h1 could be the king's rook, but if it were, then the queen's rook would have had to get out via the king's rook square, so the king (as well as the king's rook) must have previously moved to let the queen's rook by."

"The next position," continued Holmes, "illustrates a still stranger reason why castling is sometimes impossible."

"It is given that neither queen has ever moved off her own color," said Holmes. "The problem, now, is in three parts:

a—Which side, if either, can castle?

b—If the rook on g1 is removed, would that affect the answer?

c—If the rook is replaced on h1, then what would the an- swer be?"

Here is the analysis that Holmes provided us when we had all given up:

In (a), the piece captured on b6 was not the White queen (who never moved off her own color) nor the bishop from c1 (which never escaped) nor the pawn from a2, because since all three missing Black pieces must have been captured by the pawn on h6, it had no capture to make to get onto the b-file. Therefore the pawn from a2 has promoted. It had no pieces to capture, hence it promoted on a8. Hence the rook on a8 has moved, and Black cannot castle.

Now, the capture on b6 clearly occurred prior to the pro- motion (or the White pawn could not have gone by). Therefore it was not the promoted piece which was cap- tured on b6. That means the promoted White piece is now on the board (since the queen, captured on her own color, the bishop, captured on c1, and some other original piece captured on b6 account for the three missing White pieces). What is the promoted piece? Not the bishop on b5, because it could never have escaped from a8 on account of the pawn on b7. Likewise it cannot be a knight, because the pawns on b6 and c7 (the former, we recall, was there before the pro- motion) would have prevented it. Therefore the pro-

A R E T U R N VISIT

moted piece is a rook. If it is the one on g1, then the king must have moved to let it in (the pawns on g3 and h3 couldn't have cross-captured, because all missing Black pieces were captured by the pawn on h6). On the other hand, if the promoted rook is on a1, then again White can't castle. Thus White cannot castle either.

In (b), if the rook from g1 is removed, then there is no evidence that Black cannot castle; the promotion could be avoided by the White king's rook having been captured on b6, but then the king has moved to let it out. (Alternatively, the queen's rook might have been captured, and the rook on a1 could really be the king's rook.) So Black perhaps can castle, but White definitely cannot.

As for (c), in this case Black cannot castle for the same reasons as in (a), but it is possible that the promoted rook is the one on a1, in which case White can castle on the king's side.

To summarize: (a) Neither side can castle. (b) White can't castle; Black may be able to. (c) Black can't castle; White may be able to, but only on the king's side.

MYCROFT'S