Watson, tomorrow I must leave for the Continent," Holmes said unexpectedly to me one evening at Baker Street. "I am on a case of international importance, and I have no idea how long I shall be gone. It will probably be several weeks, and may be some months."
"What will I do for chess adventures?" I asked sadly. "By now, Watson," said Holmes good-naturedly, "I think you can fairly well function on your own. Just keep your eyes open and your mind alert.
"Though before I leave, Watson," he continued, "I wish to discuss with you a problem which has been on my mind and which I have been unable to solve."
"You expect me to solve it?" I asked incredulously. "No, Watson, I'm not sure that anyone can solve it," he replied thoughtfully. "Indeed, I'm not sure that it has a well-defined solution. The solution seems to lie somewhere in the borderland between chess, logic, philosophy, linguis- tics, semantics, and law."
"Sounds like a most intriguing combination," I replied. "Please let me see it."
"First I must give you a bit of historical background," said Holmes. "Recently I have been doing some research on the evolution of the game of chess. The rules have changed many times throughout the centuries. Here, it is the last change which is relevant."
"What change was that?" I inquired.
"It concerns the rule for pawn promotion. Before the last change, the rule read: 'When a pawn reaches the eighth
A N U NSO LV ED PR O BLE M
square, it is converted to any piece except a pawn or king.' However, the old rule neglected to say that the pawn must promote to a piece of the same color."
"Why would anyone ever want to promote to a piece of the opposite color?" I asked in my typically practical fashion.
"Oh, I don't know, Watson, but that's really not the point. I believe the rules of a game like chess should be abso- lutely clear and unequivocal. It certainly is not likely that one would want to promote to a piece of a different color, but it may happen in a rare case that it is to one's advantage to do so. Indeed, this did once happen, and that's why the rule was changed. It was during a tournament, and White mated Black by promoting to a Black knight."
"How did that happen?" I asked.
"Oh, it was something like this," said Holmes, and he set up the board:
"There were many more pieces on the board, but for il- lustration this position will suffice. As the position stands, White cannot win in one move if the game is played ac- cording to our present rules of promotion, but before the
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change, White wins in one move by advancing the pawn and promoting to a Black knight.
"At any rate," continued Holmes, "I really wouldn't have cared if such a case never came up in actual play. When I came across this change of rule, my first thought was what a field day it would be for retrograde analysts to compose problems according to the archaic rules of pawn promotion! I hope some future retrograder will do this.
"Then," he went on, "the following curious problem oc- curred to me. Let us say the following game was played in the old days when it was allowed to promote to a different color:
"Now, supposing it is given that it is Black's move and that Black has never moved his king. My question is: Can Black castle?"
I looked at the position, and quickly got the point: White's only possible last move was with a pawn promoting to the Black rook on a8. Now it is given that the Black king has not moved; the crucial question then is whether or not the promoted Black rook can be said to have moved.
AN UNSOLVED PROBLEM
"I wonder if the rules for castling are finely enough stated to settle that point," I suggested.
"Perhaps not, Watson, and yet I don't know! The rule for castling seems reasonably explicit: Castling is permitted provided that, one—neither the king nor the rook has moved; two—the king is not in check; three—the king does not pass over any checked square. Conditions two and three are clearly met; the whole problem lies with condition one. Now we are given that the Black king has not moved, so the whole question, as you pointed out, lies with the rook. I would tend to say that the promoted rook has not yet had time to move, hence that Black can castle."
"And I would tend to say the opposite," I replied. "I would say that the Black queen's rook was moved off the board when it was captured, and moved back on the board when it was reinstated by a promotion. So I would say that the rook has moved."
"But is it really the same rook?" asked Holmes.
Well, this is indeed a puzzler! I'm sure different readers will take different sides on this issue. Holmes and I spent most of the evening discussing it, but of course we came to no definitive conclusion. We run into this problem a bit more deeply somewhere in Part II. Meanwhile, this is an ap- propriate place to break my narrative.
P A R T II