Chess

"I'm pretty sure this was it," said Dr Watson, after setting up the position in the diagram, "only I'm not quite certain whether the black h-pawn was on h7 or h6."

Sherlock Holmes glanced at the board, then said "h6" and nudged the h- pawn one square forwards. "White's last move," he explained, "was a bishop check, yet it cannot have moved to a8 without Black having already been in check. Nor can a white pawn have promoted on a8, for that would imply a total of at least eight pawn captures by White, and there are only seven black men missing, excluding the bishop that never left f8. So the check was discovered by White's king moving from f3."

"But the king's in double check on f3," expostulated Watson.

"Indeed," said Holmes, "and the only way for such a double check to have been administered is through an en passant capture."

He moved the white king to f3, then added a black pawn on f4 and a white one on g2. "Here," he continued. "White played g4, Black captured en passant, and White took on g3. But now we see that the piece on a8 is not the bishop from f1, for, with pawns on g2 and e2, that bishop never moved. Now we must count pawn captures. On White's side, the tripled b-pawns account for three captures, plus another three to promote a pawn to a bishop on a white square. Black, meanwhile, must have made five captures to get his three f-pawns. His a-pawn must also have made a capture, since we know it was itself captured on the b-file. That's six captures, plus the bishop on f1, accounting for all White's missing men. So the question is, what happened to the white h-pawn? The only possibility is that White's h-pawn promoted to a bishop on g8, then escaped via h7. So the pawn must be on h6, not h7.

"And you saw all that in a single glance at the position," said Watson in admiring tones.

"No," replied Holmes. "I've seen the position before."