Nice post!
The Mystery of the Extra Chess Piece
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very nice. a different kind of logic puzzle
Ha ha, thanks a bunch, guys! I posted that nine months ago and I was afraid it was too intense. But it's nice to know that some of you enjoyed it! =)
There are a few more (much easier) chess puzzles on my puzzle page at http://www.philipbrocoum.com/?page_id=228 if you're interested.
Oh, and in case anybody is interested, the position in the puzzle actually is possible to get to. One possible way of reaching the position:
1. g4 h5 2. g5 Nh6 3. gxh6 g6 4. h7 Rg8 5. h8=B Bg7 6. c4 Bd4 7. c5 Be3 8. c6 a5 9. Nh3 Ra6 10. Nf4 Bxf4 11. Rg1 Rb6 12. Rg3 Rb5 13. Rh3 Rc5 14. Bc3 Na6 15. Qa4 Nb4 16. Kd1 Nd3 17. Qe4 Nxc1 18. Ke1 Nd3+ 19. Kd1 Nb4 20. Ke1 Be3 21. Qh4 Na6 22. Kd1 Nb8 23. Kc1 e5 24. Kd1 Qe7 25. Kc1 Qd6 26. Kd1 Qd5 27. Kc1 Qb3 28. Rg3 Qa3 29. Rh3 Kf8 30. Rg3 Kg7 31. Rh3 Re8 32. Rg3 Re6 33. Rh3 Rf6 34. Rg3 Rf5 35. Rh3 Rg5 36. Rf3 Rg1 37. Rh3 Kf8 38. Rf3 Ke8 39. Rh3 Rxf1+
Logic really works, lol!
Mate in 1
This is what it would be like to play chess with Sherlock Holmes! Very nice puzzle - and very enlightining!
Took me 10 minutes to figure out, here is a condensed version.
It's the g2 pawn, because:
The position of White's Bishop is impossible, so either that Bishop or one of White's pawns must have been the piece. White is in check, so it's his turn and Black's last move must have been to take White's Bishop on f1. But White's Rook had to come out first, and the only way is to move the g2 pawn. The h2 pawn could not have promoted into White's Bishop on c3 since it is dark-squared, and only one of Black's pieces is missing, and reaching a dark promotion square with only one capture is possible for the g2 pawn only.
Nice retrograde analysis.
This puzzle is the purest form of deductive logic, while the game of chess itself is logic of a much more chaotic nature :)
Isnt there a book written abou this, with Holmes teaching Watson? I have the book...nice one! Loved it!
Good puzzle.
Nice post. Glad I came across it.
Thanks for the kind words, everyone!
The book you are thinking about, jkudria4145, is Chess Mysteries of Sherlock Holmes: Fifty Tantalizing Problems of Chess Detection by Raymond Smullyan: http://www.amazon.com/Chess-Mysteries-Sherlock-Holmes-Tantalizing/dp/0812923898
It is, indeed, where I got the idea for this puzzle. Raymond Smullyan is a rather famous logician and puzzleist. All of his books are great.
Ha ha Justified08, that's perfect! Proof that this position is – technically – possible to achieve in a real chess game :-)
from chess mysteries of sherlock holmes,
http://www.amazon.com/The-Chess-Mysteries-Sherlock-Holmes/dp/0486482014
My friend and I were playing chess the other day, and while he was admiring some birds in the park I pulled a fast one and stuck one of my pieces back on the board. Unfortunately, my new-found criminal career was doomed from the start, for he quickly noticed my deception.
“Did you see me out of the corner of your eye?” I asked.
“Yes,” my friend admitted, “but to tell you the truth, I would have known even if I was a complete stranger just passing by.”
I laughed. “Don’t be silly! A stranger wouldn’t even know who’s turn it is, let alone that there is an extra piece on the board.”
“It’s the power of logic, my friend,” he said with a smile. He then proceeded to embark upon the most fascinating journey of deduction that I have ever heard. Twists and turns abounded at every corner! And, at the end, he managed to prove with mathematical precision exactly which piece on the board should, in fact, not have been there.
Before I continue with the story, I urge you to look at the board below and see if you can figure out which piece is the extra piece. Do not assume that my friend and I played smart chess, only that we followed the rules. Also assume that there is only the one error on the board.
“Ok,” I said, “Prove it. Who’s turn is it?”
“Must you start off so easy?” said my friend. “White is in check, therefor black must have moved last.”
I took a quick glance at the board and conceded the point. “Ok, but that doesn’t mean there is an extra piece.”
“Look at the bishop on c3. How did it get there?”
I saw that the bishop was a dark-squared bishop that should have come from c1. “The pawns on d2 and b2 haven’t moved, so the bishop could not have gotten to c3. Dear heavens, did we screw up our game?”
“Not at all. The bishop on c3 must be a promoted bishop. It is the only explanation. White must have promoted one of his pawns to a bishop.”
“There is another possibility,” I said. “Maybe we just screwed up and the bishop shouldn’t be there.”
“No,” said my friend, “the bishop is needed because without it the white king is in check from two places at once.”
“Oh. Never mind. I still do not see why there must be an extra piece.”
“We know that white promoted a pawn to a bishop, but there are 8 white pawns on the board. Thus, one of the white pawns should not be there.”
I felt a smile creeping to my face. Perhaps my friend was on to something after all. “Go on…”
“The extra pawn can’t be b2 or d2 for the same reason the extra piece couldn’t be the bishop; without those two pawns the white king is in check from two places at once.”
“I see!” I exclaimed. “We have proven the existence of an extra piece, and we have narrowed down our list of suspects to six pawns. But what now? None of the other pawns are needed.”
“It’s true that we cannot deduce much more about the white pawns, so let’s focus on the other pieces. There are three white pieces not accounted for: the two original bishops and one of the knights. Can you tell me how many of these white pieces were captured by black pawns?”
I thought really hard. “Well, the black pawns are all on their original files—”
“Or the g and h pawns could have switched places!”
“—right. Or those two pawns switched places. Since there are only three white pieces missing, the black pawns must have captured either 0 or 2 pieces. An odd number of captured pieces would have left two black pawns on the same file.”
“You are almost there,” said my friend. “Which is it? 0 or 2?”
“I have no idea,” I admitted.
“No worries. Let’s take this one piece at a time. Did a pawn take the original white bishop on c1?”
“No! The white bishop on c1 never moved from that square because it’s locked in by the pawns on b2 and d2.”
“Good! Now, what about the bishop from f1? Did a pawn take it?”
“No!” I exclaimed. “That bishop is also locked in by pawns.”
“Be careful,” said my friend. “The pawns on b2 and d2 are necessary to keep the king from being in check from two places at once. However, the pawns that are locking in the white bishop from f1 are not necessary. Either one of e2 or g2 could be the extra piece that shouldn’t be on the board. If that is the case, the white bishop could have moved to another part of the board where it was taken by a black pawn.”
“Oh,” I said, very sadly. “So, what gives?”
“Let’s go back to the very beginning of our deduction. Black just moved his rook to put white into check. Where did his rook move from?”
“The situation seems almost impossible. The only possibility is that black’s rook took a white piece on f1 after moving from either g1 or h1.” Suddenly, it came to me (or so I thought). “Black’s rook must have taken the white bishop on f1!”
“Again, be careful,” my friend warned. “If white’s bishop was on f1, how did the black rook get to g1 or h1 in the first place? And, for that matter, how did the white rook get out?”
“Well, I suppose that means the g2 or h2 pawn must be the extra piece, because there had to have been a hole for the rooks to get through.”
“I’ll say it once more, be careful. Try out this scenario: The e2 pawn is the extra piece. At some point in the game, the f1 bishop left its home square. At another point in the game, the black rook moved to g1 or h1. Finally, at a third point in the game, the black rook was blocked by a white knight. In this scenario, the last move was the black rook taking the white knight.”
“Ok, ok,” I moaned, “but it doesn’t matter. In any case, the black rook took something. Maybe it took the white knight, and maybe it took the white bishop. But it took something.”
“Not necessarily. There is one more possibility. What if the f2 pawn is the extra piece? In that case, the rook could have simply moved to f1 from anywhere along the f file. No capturing is necessary.”
“^*$&!” I exclaimed.
“Don’t worry, Phil. It all works out nicely in the end. In this final scenario, with the f2 pawn being the extra piece, what do we know about the f1 white bishop?”
I quickly came to my senses. “We know it never left its home square. If the f2 pawn should not be there, then the e2 and g2 pawns should be, thus locking in the white bishop.”
“Exactly! In that scenario, nobody knows what happened to the white bishop from f1. All we know is that it never left its home square and thus could not have been captured by a pawn.”
“Whew,” I breathed. “Can you sum that up for me?”
“Sure. When you boil it all down, here is what we have:
My friend finished speaking and I could feel my head spinning. “Wow,” I said. “All that trouble only to prove that no black pawn did any capturing. What good does that do us?”
“What good does it do?” said my friend. “Why, it’s only the key to the entire mystery!”
“Then please share it.”
“If none of the black pawns moved off their home file, how did a white pawn get through to promote to the c3 bishop?”
“One of the white pawns must have moved diagonally by making a capture.”
“And how many black pieces are missing?”
I saw where my friend was going. “Only one black piece is missing! Therefor, one of white’s pawns moved exactly one diagonal in order to move around a black pawn and make it to the 8th rank.”
“So, Philip, how does that narrow our list of suspects?”
“We already know that it wasn’t pawns b2 or d2. Now we know it must have been a pawn that could only make one diagonal move. That rules out a2, because it would have to make two captures to get around a5. It rules out c6, because it would have to make two captures to get to either the a file or the e file. It rules out e2 because it would need two captures to get around e5.”
“What is left?”
“There are now only three possibilities: the f2 pawn promoted on e8 or g8, or the g2 pawn promoted on h8, or the h2 pawn promoted on g8. We are getting really close!”
“Very close indeed, Philip. There are three possible squares that the pawn could have promoted on: e8, g8, and h8. What do you notice about the color of those squares and the color of the promoted bishop?”
I literally gasped as the final piece of the puzzle fell into place. “The promoted bishop is a dark-squared bishop. If the pawn had promoted on e8 or g8, it would have been a light-squared bishop. The only pawn that could have reached h8 with only one diagonal move, and thus could have promoted to a dark-squared bishop, is the g2 pawn!!!! The mystery is solved! The g2 pawn should not be on the board because it was promoted to the bishop on c3!”
My friend got up to shake my hand. “Well done, Philip. I knew you had it in you. Now, remove that nasty pawn and let me get back to whipping your butt. It’s your turn. Mate in…”