“No, never. It would then be in check to the white knight on b1, which, given its position, is clearly not a recent arrival, but must have got there several moves ago.” Munoz looked at them both. “So it’s another case of imaginary check showing us that it wasn’t the king that moved.”
“Therefore the last move,” said Julia, “was made by the black queen.”
The chess player looked noncommittal.
“That, in principle, is what we must assume,” he said. “In terms of pure logic, once we’ve eliminated the impossible, what remains, however improbable or difficult it may seem, must be right. Moreover, in this case we can prove it.”
Julia looked at him with new respect.
“This is incredible. Like something out of a detective novel.”
Cesar pursed his lips.
“I’m afraid, my dear, that’s exactly what it is.” He looked at Munoz. “Go on, Holmes,” he added with a friendly smile. “We’re on tenterhooks.”
One corner of Munoz’s mouth twitched humourlessly, a mere polite reflex action. It was clear that all his attention was taken up by the chessboard. His eyes seemed even more deeply sunk in their sockets and there was a feverish gleam in them: the expression of someone absorbed in contemplating imaginary, abstract spaces that only he could see.
“Now,” he suggested, “let’s look at the possible moves the queen could have made, positioned as she is on square c2. I don’t know if you’re aware, Julia, that the queen is the most powerful piece in the game. She can move across any number of squares, in any direction, imitating the movement of all the other pieces except for the knight. As we can see, the black queen could have come from four possible squares: a2, b2, b3 and d3. By now, you can see for yourself why she couldn’t have come from b3, right?”
“I think so.” Julia frowned in concentration. “I presume she would never have left a position where she had the white king in check.”
“Exactly. Another case of imaginary check, which discounts b3 as her possible origin. And what about d3? Do you think the queen could have come from there, for example, to avoid the threat from the white bishop on fl?”
Julia considered that possibility for a while. At last her face lit up.
“No, she couldn’t, for the same reason as before,” she exclaimed, surprised to have reached that conclusion on her own. “On d3, the black queen would have been holding the white king in another one of those imaginary checks, right? That’s why she couldn’t have come from there.” She turned to Cesar. “Isn’t this fantastic? I’ve never played chess in my life.”
Munoz was pointing his pencil at square a2 now.
“It would be another case of imaginary check if the queen had been here, and so we can discount that square too.”
“Then it could obviously only have come from b2,” said Cesar.
“That’s possible.”
“What do you mean ‘possible’?” Cesar was confused and intrigued at the same time. “It looks obvious to me.”
“In chess,” replied Munoz, “very few things can be termed ‘obvious’. Look at the white pieces along line b. What would have happened if the queen had been on b2?”
Cesar stroked his chin thoughtfully.
“She would have been under threat by the white rook on b5. That’s probably why she moved to c2, to escape the rook.”
“Not bad,” conceded Munoz. “But that’s only a possibility. Anyway, the reason she moved isn’t important to us at the moment. Do you remember what I told you before? Once the impossible has been eliminated, what remains must, of necessity, be right. To sum up, (a) Black has just moved, (b) nine of the ten black pieces on the board could not have moved, (c) the only piece that could have moved was the queen, (d) three of the four hypothetical moves by the queen are impossible. Therefore, the black queen made the only possible move: it moved from b2 to c2,
“Very,” said Julia, and Cesar agreed.
“That means,” Munoz went on, “that we’ve managed to take the first step in this reverse chess game that we’re playing. The subsequent Position, or rather, the previous position, since we’re working backwards, would be this.”
“Do you see? The black queen is still on b2, before its move to c2. So now we have to find out what move White made that obliged the queen to do that.”
“It must have been the white rook,” said Cesar. “The one on b5. The treacherous devil could have come from any square along row 5.”
“Possibly,” replied Munoz. “But that doesn’t entirely justify the queen’s flight.”
Cesar blinked, surprised.
“Why not?” His eyes went from the board to Munoz and back to the board again. “The queen was obviously fleeing the threat from the rook. You yourself said so a moment ago.”
“I said that
“I’m lost,” confessed Cesar.