Little Question Of Location

Another stroll to the chess club?" Holmes asked me some days later.

"Why, certainly," I replied, delighted with the possibility of another little adventure.

When we arrived, two gentlemen unknown to us were playing a game. The position was as follows:

Black-9

JL

i

i

i

â

S â

i

ink

hp g

â â

* K

*

White-11

A White pawn had been carelessly placed on the border between g2 and h2. I was about to inquire on which of the two squares it was supposed to stand when Holmes held up his hand to me. I realized that perhaps he could deduce the answer and would like to surprise the players by demonstrating this. So I remained silent and watched his expres sion with eager anticipation. But Holmes said nothing, and once or twice shook his head a bit hopelessly.

Just then, White placed his hand on a piece and was about to move. "Just a moment, please," said Holmes eagerly. "Would you be so good as to tell me whether this game has been a normal game?"

"A normal game?" asked White, astonished. "Just what, sir, do you mean by a normal game?"

"Oh," replied Holmes, "by that I simply mean a game in which no pawn underpromotes, a game in which a pawn promotes only to a queen."

"Why, yes," replied White, "this game has been what you call 'normal.' Indeed, so far there have been no promotions at all."

"Ah! Then please permit me," said Holmes, as he leaned over and moved the White pawn to the correct square.

"Thank you," replied White, as he was about to resume play. But suddenly he looked up at Holmes in amazement. "Why, how did you know, sir? How did you know where the pawn lay?"

"Because you were kind enough to tell me," laughed Holmes, who was evidently enjoying this little mystification.

"I told you?" replied White, more astonished than ever.

"Why, yes," replied Holmes. "Not explicitly, to be sure, but implicitly. You told me not directly, but by implication."

This remark did not appear to enlighten the players overmuch. Holmes continued, "I soon saw that from the position alone, it was not possible to place the pawn correctly; there were three things I had to know. First, I did not know for sure which side was White—though, of course, I could make a pretty good guess. Second, I did not know whose move it was. Third, I did not know whether there had been any underpromotions. Well, when I saw one of you place his hand on a White piece to move it, then of course 1 knew which side was White and that it was White's move. As to the matter of underpromotions, you yourself were kind enough to tell me. So where is the mystery?"

"But," said Black, "what has all this to do with the location of the pawn?"

"Oh," said Holmes casually, "that was the elementary part, you know. I reasoned as follows:

"Black has just moved; what was his last move? Obviously with the king or one of the knights. It could not have been with either knight, for neither one could have moved from a square which would not be checking the White king. Therefore it was the Black king. It obviously did not come from b3 or d3, nor did it come from d2, since it would then have been in imaginary check from the White bishop. Therefore it came from b2, moving out of check from the White rook. How did White deliver this check? He could not have moved his king away from b4, for he would have been in imaginary check from the pawn on a5. Nor, of course, could he have moved his king from b3. Could it be that the rook itself moved last from c5, d5, or e5 and gave the check directly? Well, considering the other White rook on b6, only if the checking rook captured a Black piece on b5. What Black piece could this be? Not a knight, since there are two Black knights on the board, and there have been no underpromotions. Also, not a bishop, because the Black bishop moving on white squares is still on c8. Also not a pawn, because the pawn on a5 comes ultimately from c7, hence no pawn from e7, f7, g7, or h7 could possibly get to b5. Also not a rook, because the rook from a8 could not have gotten out onto the board, but must have been captured on a8 or b8, since neither the bishop on c8 nor the pawns on a7, b7, and d7 have yet moved. The last possibility to examine is the Black queen. This, too, is not possible, because it would have been checking White and could not have come from any square which would not be checking White—even assuming that the rook, in capturing her, had come as far as from e5.

"Thus White's last move was not with the rook on b5. Therefore Black's last move was with the king from b2, capturing the White piece on c2, which had just discovered check from the rook. This White piece could only be a knight from b4 or a bishop from b3. The former is out, since there are two White knights on the board, and there haven't been any underpromotions. Therefore Black's last move was with his king on b2, capturing a White bishop on c2. The home square of this bishop is f1, hence the pawn between g2 and h2 must really be on h2, otherwise the bishop couldn't have left its home square. That, gentlemen, proves that the pawn is on h2."

"An admirable chain of reasoning," remarked White.

"Did you say," said Black, "that this was the elementary part?"

"Well," replied Holmes, in a sort of mischievous half-apology, "perhaps I should have said fairly elementary."

A moment later Holmes continued, "Actually, gentlemen, this position is almost identical with one I came across some time ago." Using a board and chessmen from a nearby vacant table, he set up the following:

Black-9

A

i

i i

â

S á

i

S

â

âèâ

4X4

White-11

"The conditions are the same as before—that is to say, it is White's move and there have been no underpromotions. The position differs from the preceding in that the pawn which was previously placed ambiguously now stands definitely on g2, whereas the pawn which previously stood definitely on c6 is now placed ambiguously between c6 and d6. The problem is: Does this pawn stand on c6 or d6?"

"Why, on d6, of course," replied one of the two players instantly. His name was Fergusson, and we later found him to be an excellent logician.

"Why?" inquired Holmes

"Because," replied Fergusson, "if it were on c6, we would have the same impossible situation as before."

"Capital," replied Holmes, "but I would like a little more information than that. What I really wish to know is, how does the pawn being on d6 rather than c6 relieve the impossibility?"

"I'm afraid," replied Fergusson, "that your question is not sufficiently precise to admit of a precise answer."

"True, true," replied Holmes. "Well then, let me put the question to you this way: Exactly what was the last move White made?"

"That is a precise question," replied Fergusson. "Let me see now. Ah yes, very pretty! What happened was this: The same argument as before establishes that if the Black king just captured a White piece on c2, this piece could only be a bishop. But it can't be a bishop, because of the pawns on e2 and g2. Therefore Black's last move was with the king from b2 to c2, but it did not capture a piece. Therefore White's last move must have been with the rook on b5 moving horizontally and capturing a Black piece on that square. What was the Black piece? By the same argument as before, it couldn't be a pawn, knight, bishop, or rook. But a pawn on d6 rather than c6 invalidates the preceding argument that it couldn't be a queen. It could have—indeed it must have— been a queen, which gave check to the White king by coming from c6. But this is possible only if the White rook now on b5 had been standing on c5. Therefore, White's last move was with the rook on b5, moving from c5 and capturing a queen on b5."*

"Excellent reasoning," said Holmes. "I do hope, Mr. Fergusson, we shall have the pleasure of seeing you again."

Holmes and I were just about to leave the club when he stopped at one of the many deserted chess tables on which there was an unfinished game. "Halloa," he said, "this may be interesting. Mr. Fergusson and Mr. Fenton," he called, "if you wouldn't mind stepping over here a moment, I think we may have another intriguing position to analyze. Again we have an ambiguously placed pawn, but this time vertically rather than horizontally." We studied the position:

Black-13

1

Ht $ 4 I

i

*

iiii

i

t

A

8

ê

I

È

if È 1

g

White-13

* If the reader finds this explanation difficult to follow, I suggest that he put the Black king on b2, the White rook now on b5 on c5, the ambiguous pawn on d6, and a Black queen on c6—this is how the position was three moves ago. Then the following sequence takes us to the present position: (1) Black queen to b5, check; (2) rook on c5 takes queen; (3) king to c2.

"I wonder," Holmes continued, "if we can deduce on which square it stands? I think we can safely assume that the White is as indicated."

At first, I must say, it looked quite hopeless to me! But the four of us carefully studied the situation together, and gradually the following solution came to light.

Both White's queen's bishop and Black's king's bishop were captured on their home squares. Hence the captures on b6 and c6 were of White's king's bishop and knight— clearly the bishop was captured on c6. The captures by the White pawn on g3 and the one on the f-file (f4 or f5) were of Black's queen's bishop and knight; obviously the pawn on the f-file captured the bishop. Now, Black's queen's bishop did not get out onto the board until after the capture on c6. So White's king's bishop was captured before Black's queen's bishop. The pawn on f-file comes from e2; it moved before White's king's bishop got out and was captured. It couldn't have captured on f3, because Black's queen's bishop hadn't got out yet to be captured. Hence it moved from e2 to e4 and later captured Black's queen's bishop on f5.

The sequence was this: Pawn from e2 moved to e4, then White's king's bishop got out to be captured on c6, then Black's queen's bishop was captured on f5. So the White pawn must be on f5.

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