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Coyote
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 Posted: Fri Feb 04, 2005 7:01 am Post subject: 1 |
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Here's a simple little diversion to waste a couple of minutes on. White to play and mate in one move. (The position may look a bit improbable but I assure you it's perfectly legal)
T. R. Dawson, 1929
What's that--you say there's no one-move checkmate? Ah yes, how careless of me--I left off one of the white pieces. There should be a second knight on...ummm...
Hang it all, I can't seem to remember! Just where does that other white knight get placed? |
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LoudmouthLee
Member of the Year
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| Posted: Fri Feb 04, 2005 7:16 am Post subject: 2 |
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That pesky knight to remember belongs in a4 and the mate move is Qxb2++
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-LmL
I'm sorry. I have no desire to talk to you. |
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Lucky Wizard
Daedalian Member
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| Posted: Fri Feb 04, 2005 7:20 am Post subject: 3 |
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As nearly as I can tell, there are two solutions.
The more interesting solution is knight on a4, as it makes it so that QxQ is mate.
I keep checking to see whether there's anything wrong with the other one, because it seems uninteresting enough that I think the creator would've tried to eliminate that possibility, and it means the solution's nonunique, but I can't find anything wrong with it, so here it is: knight goes on a5, b6, d6, or e5; NxR is mate. |
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LoudmouthLee
Member of the Year
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| Posted: Fri Feb 04, 2005 7:24 am Post subject: 4 |
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Lucky... your second mate is correct as well. I liked mine better, though 
_________________
-LmL
I'm sorry. I have no desire to talk to you. |
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Coyote
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| Posted: Fri Feb 04, 2005 7:27 am Post subject: 5 |
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| There is only one correct square for the knight. The real puzzle is figuring out just why the other squares can't be right. |
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LoudmouthLee
Member of the Year
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| Posted: Fri Feb 04, 2005 7:37 am Post subject: 6 |
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| Lucky Wizard wrote: |
As nearly as I can tell, there are two solutions.
The more interesting solution is knight on a4, as it makes it so that QxQ is mate.
I keep checking to see whether there's anything wrong with the other one, because it seems uninteresting enough that I think the creator would've tried to eliminate that possibility, and it means the solution's nonunique, but I can't find anything wrong with it, so here it is: knight goes on a5, b6, d6, or e5; NxR is mate. |
Okay, knowing this that some of the other spaces are "wrong" here's what I have:
Those black pawns up top prohibit b6 and d6 from being logical places. Why didn't black take the piece the move before? So there we have eliminated two of those situations. Still, though, we have a5 and e5 (NxR) or a4 (QxQ)
The next move to eliminate is a4. I might be barking up the wrong tree here, but it would be VERY difficult to resist having that Knight there and NOT taking the queen sooner. That trade would have let white not get into this hairy situation to begin with.
That leaves a5 and e5 as possibilities.
Bah. My head hurts. Any help?
_________________
-LmL
I'm sorry. I have no desire to talk to you. |
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Tahnan
Daedalian Member
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| Posted: Fri Feb 04, 2005 8:55 am Post subject: 7 |
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| LoudmouthLee wrote: |
Okay, knowing this that some of the other spaces are "wrong" here's what I have:
Those black pawns up top prohibit b6 and d6 from being logical places. Why didn't black take the piece the move before?... |
Patzers! Are you really trying to work out the psychology of two players who got themselves into this mess? Logic. Pure logic. Observe:
This is a legal position, we’re told, and it’s White’s move. What was Black’s last move? Possibly a move with the pawn at f4 (advance or capture); possibly a capture with the pawn at b4; possibly Na6. White’s move before that? Possibly a capture at b5; possibly with a captured piece; possibly with the king to d3, if Black just moved his pawn to f5; or possibly, of course, with the missing knight.
Black is missing two pieces (a pawn from the right side of the board and the black-square bishop); White is missing two pieces (the pawn from g2 and a rook). Note that two black pawns are farther down the board than a white pawn on the same row, and that two white pawns are doubled.
From the latter fact, we know that one of Black’s missing pieces must have been captured on the b file. The sequence of events on the left side of the board must have been: Black’s b pawn moves to b4; White’s a pawn captures a4 to b5; Black’s a pawn advances to a2. Since the capture happened on a white square, it cannot have been the missing bishop; it must have been either the pawn from g7, after it promoted and moved to b5, or else it was another piece entirely, which has been replaced by a promoted pawn. Either way, Black’s pawn from g7 promoted.
How did it get to g1? Since the black pawn on d2 had to capture twice to get there, the g7 pawn didn’t capture to get past the white g pawn. Nor was the white g pawn captured on the g file, since the pawn at d2 did all of Black’s capturing. The only way the white pawn could get out of the way of the black pawn and also disappear is for it to capture once to get off its own file (and not capture again, since White’s only other capture was on b5), promote, and get captured later. So here the sequence is: white g pawn captures onto f or h, and then it and Black’s g pawn promote. So it couldn’t have captured onto h, since it could only get past the h pawn if it captured from g7 to h8, in which case it couldn’t have gotten out of the way of the black g pawn; and therefore it captured onto the f file. Since it didn’t capture from g7 (see above), but it did capture the black bishop, the pawn’s move was to capture the black bishop on f6, and to later promote on f8, and get cpatured by the d2 pawn. Meanwhile the g7 pawn moved down and promoted on g1.
This means that Black’s f pawn must have been on f5 for a while, so that the white pawn could capture to f6 and move forward to promote. So Black didn’t just move the pawn, and thus his last move was knight to a6, and the only square it could have come from is b8.
So what was White’s move just before that? Not with the king after all, which would have been in check. Not with a captured piece, since the black pawn’s captures happened a while ago. Could White have just captured at b5? Of course not; the pawn at a2 had to get past it a while ago. That means that White’s last move was with the missing knight.
That's as far as I can get at 4 in the morning after one martini. If no one's finished this off by tomorrow, I'll mix another martini and tackle the rest of the logic. |
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L'lanmal
Daedalian Member
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| Posted: Fri Feb 04, 2005 4:42 pm Post subject: 8 |
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Using that we know that the square is unique, we know which one it is. (The rest of the positions could be reached from each other by black moving his knight back and forth while white moves his knight.)
Other than that, I haven't really gotten farther than Tahnan.
If black's last move is with his knight, and white's previous move was with his missing knight, then the black move prior to that would have to be with his knight as well (by the previous reasoning), right?
So Black's last non-knight move came prior to white's capture at B5. That capture was of a Rook, knight, or queen, since black's promoting square G1 is black and B5 is white.
Immediately prior to the capture, what could be black's last move of significance (ignoring a stalling knight move)? It isn't pawn to B4, since then B5 would've been vacant. So I *think* it is with the captured piece to B5.
Perhaps there is a way to determine what color of square white's knight was on at this point?
Also of note is that I think Black's king made it to A3 before white's queen was moved to C3. White's pawn was on A4, so Black's king had to come via B4. This also means that the black pawn had not advanced to A4 yet, FWIW. |
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Guest2
Guest
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| Posted: Fri Feb 04, 2005 4:59 pm Post subject: 9 |
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| This is all a little over my head. Can someone please explain what, precisely, is wrong with placing the missing Knight at A5 to mate Black with NxR? |
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Tahnan
Daedalian Member
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| Posted: Fri Feb 04, 2005 5:58 pm Post subject: 10 |
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Guest2: not yet I can't. But there are (at least?) four squares on which the knight could be sitting which would give a mate in one. However, since we're told that this is a legal position, it remains to be seen which of those squares we can put the knight on to make a legal position.
For instance, if you'll forgive a somewhat clumsy example (and I hope it works), but the best I could do impromptu:
It looks like Black has mated White, but in fact it's only mate in 1, as Black still has a bishop on the board that I forgot to place. What's Black's checkmating move?
Answer: The bishop has to be between the queen and the king. If it's on a2, the move is Bb3++ (not Na3+, as the king could capture the bishop on a2, and the knight can't discover check to any other square); if it's on a3, the move is Bb4++ (as the knight now can't discover check at all).
But notice that all eight black pawns are still on the board. That means that the missing bishop isn't a promoted bishop. And notice that the black-square bishop can't have moved off its home square, since the pawns are still blocking that square. Consequently, there's no way that the missing bishop is on a black square, and thus it must be on a2.
Therefore, one might ask "why can't the missing bishop be on either a2 or a3?" The answer is that only one of those two options would result in a legal position.
So that's the challenge that Coyote (well, Dawson, really) has posed to us: where can we put the knight so that there's a mate in one, and so that the position is legal? |
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borschevsky
Chessnut
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| Posted: Fri Feb 04, 2005 7:49 pm Post subject: 11 |
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| L'lanmal wrote: |
| So Black's last non-knight move came prior to white's capture at B5. |
That can't be, because the black a2 pawn can't get there until after white plays axb5. |
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Courk
Daedalian Member
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| Posted: Fri Feb 04, 2005 8:31 pm Post subject: 12 |
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| Tahnan, in your example you said "Consequently, there's no way that the missing bishop is on a black square, and thus it must be on a2." Shouldn't that be white square? |
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fadeblue
Daedalian Member
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| Posted: Fri Feb 04, 2005 8:52 pm Post subject: 13 |
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| Tahnan: Why couldn't the white pawn have captured at b4 instead of b5? |
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borschevsky
Chessnut
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| Posted: Fri Feb 04, 2005 9:00 pm Post subject: 14 |
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| Because then there's no way to get the black pawn to b4. |
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fadeblue
Daedalian Member
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| Posted: Fri Feb 04, 2005 9:38 pm Post subject: 15 |
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| Oh, oops. Okay, I guess I should read more carefully then. |
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L'lanmal
Daedalian Member
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| Posted: Sat Feb 05, 2005 2:23 am Post subject: 16 |
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My mistake... how about this then?
| Quote: |
Since it didn’t capture from g7 (see above), but it did capture the black bishop, the pawn’s move was to capture the black bishop on f6, and to later promote on f8, and get cpatured by the d2 pawn. Meanwhile the g7 pawn moved down and promoted on g1.
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How about the d2 pawn takes the white rook and a white knight to get into position. Then the white king moves into position (with the rest of the pieces). After this, black moves his F pawn out, and the white pawn takes the bishop and promotes to the mystery knight at f8.
Likewise, the black pawn at g1 promotes to the knight that eventually gets to a6, replacing the one the white pawn took at b5.
This is the only way I can see the pieces getting situated as they are in the lower left.
After PxB is played, the white pawn is at f6, and the black at g6. Black then plays p-g5. Notice that it is white's turn, and the pawns are on the same color. Each pawn move from here on is from a white square to a black square, or vice versa. Every knight move is from a white square to a black square, or vice versa. So every time it is white's move (unless a different piece is moved) the two knights will be on the same color square.
In the final position, possible mates come from a knight at a4, a5, b6, d6, or e5. The black knight is on a6 (a white square). So the white knight can only be at a4 (the only white square listed).
Last edited by L'lanmal on Sat Feb 05, 2005 4:25 am; edited 1 time in total |
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Tahnan
Daedalian Member
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| Posted: Sat Feb 05, 2005 3:29 am Post subject: 17 |
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| Yes, I did reverse "black square" and "white square" in my mini-problem, primarily because I designed it in a table in MSWord, so I had to work out the color of the square by counting and hoping. |
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Jedo the Jedi
Paragon in Training
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| Posted: Sat Feb 05, 2005 3:37 am Post subject: 18 |
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I don't know if the answer has been decided on and proved, but my only logical guess is e5. I'm not very good at these types of puzzles, however, that seems like the best place.
I'm not going to go way back, but before that, it could have been on g4 which caused that pawn to come down. The a4 and a5 position just don't seem logical because of the 'what was black's last move?' line of thought.
If there is a flaw in my plan, please point it out, and if I missed someone's post where they already shot this down, then I'm sorry. |
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i_h8_evil_stuff
Daedalian Member
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| Posted: Sat Feb 05, 2005 4:06 am Post subject: 19 |
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*glances at Tahnans board for 2 seconds*
[It's sideways.]
_________________
Space for sale. PM i_h8_evil_stuff for details. |
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Tahnan
Daedalian Member
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| Posted: Sat Feb 05, 2005 5:52 am Post subject: 20 |
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| Uh. So yes, I didn't switch "black square" and "white square" when I counted squares. Instead, I inadvertantly rotated the chessboard 90 degrees. But I have no clue how that happened. Anyone? |
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Coyote
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| Posted: Sat Feb 05, 2005 10:17 am Post subject: 21 |
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Looks like L'lanmal has this one wrapped up. Equal credit to Tahnan for a thorough preliminary analysis. Nice work, both of you! Next time I post one of these looks like I'll have to pick something a little more difficult. 
As for that sideways board...I'm boggled. I didn't think it was even possible to do something like that. If you ever figure out how you did it, let me know (I might find a use for it someday!) |
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referee
June 21st, 2004 Member
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| Posted: Sat Feb 05, 2005 12:57 pm Post subject: 22 |
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I more or less followed Tahnan's explanation, but the final bit by L'l still escapes me. Can you explain that again?
_________________
Jan 21st, 2008: The pillaging continues.
Mar 4th, 2008: Rest in Peace, Gary Gygax. May your dice always roll a natural 20 wherever you are.
Be the Ultimate Ninja! Play Billy Vs. SNAKEMAN today! |
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Jedo the Jedi
Paragon in Training
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| Posted: Sat Feb 05, 2005 2:41 pm Post subject: 23 |
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| L'lanmal, how would the white knight have gotten there? I read through your post almost a dozen times, but I didn't see it. Maybe I missed it. |
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L'lanmal
Daedalian Member
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| Posted: Sat Feb 05, 2005 6:44 pm Post subject: 24 |
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Consider only this portion of the board:
and ask yourself not what black's last move was, but instead ask "What was the last move by either side in this section of the board?"
Definately not the pawn at f2, which never moved. Not the pieces at a1, b1, c1, d1, e1, a2, b2, c2, d2, e2, b3, c3, e3, c4, or c5, which had no square to come from. Not a capture by the black pawn at b4, since all black captures have been accounted for by black's d pawn. (See Tahnan).
That leaves the kings and the white pawn capture at B5. Both Tahnan and Borschevsky explained to me the pawn capture could not be last since then the black pawn could not get to a2. The black king at a3 could have come from a4, but that square is in appearant check from b3. That means the white pawn would have to move b2-b3 when the black king was already at a4, then the black king moves to a3. But this could not be the LAST move since the black queen would still need to get to b2.
The only remaining possible last move in this section of the board is Ke4-d3. So this must be it. This means the black pawn is not yet at f5.
We must remember that Ke4-d3 is the LAST move made by any of the pieces in that section of the board. All those pieces are in place, and aren't touched again.
Now, step back and remember what captures have taken place. The white pawn has captured something at b5. The black pawn at d2 made two captures to get there... a white rook and something else.
Since the black pawn is not yet at f5, neither white nor black have promoted yet. So what could those captures have been of? Definately none of the pieces we have in the bottom left of the board have been captured. No promoted pieces have been captured, since nothing has been promoted. That leaves only a black knight and a white knight.
It follows that the black knight at A6 is a replacement from the g pawn promoting, as is the missing white knight.
So lets rewind the game to right around when white played Ke4-d3. The white g pawn might have been in a different position, but it looks something like this:
At some point, black plays Pf5(+), followed by B-f6 allowing white to capture and both sides to promote. But when white plays PxB, look at what squares the white and black pawns are on. White just moved and is on f6. Black's is on g6, and will play to g5. Black has no other pieces he can move: the bishop is gone, the lower left is finished, and the remaining pawns never move. White has no other pieces he can move either. So they alternate moving their pawns which promote to knights. Then they move their knights.
There are many ways their knights can get into position after this. The important thing is: Whenever it is white's turn, his piece is on the same color square as black's. First f6 and g5. Then f7 and g4. Then f8 and g3. Etc.
One path the white knight can take to get to a4 is F8-D7-A6-A4. Another is F8-E6-D8-C6-B8-D7-B6-A4. Any such path will take an even number of moves. Any path to A5, B6, D6, or E5 would take an odd number of moves.
The final step is to determine that white's knight ended on a black square (a4), since black's knight ended on a black square (a6). |
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referee
June 21st, 2004 Member
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| Posted: Sat Feb 05, 2005 7:29 pm Post subject: 25 |
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ah, I got it now.
_________________
Jan 21st, 2008: The pillaging continues.
Mar 4th, 2008: Rest in Peace, Gary Gygax. May your dice always roll a natural 20 wherever you are.
Be the Ultimate Ninja! Play Billy Vs. SNAKEMAN today! |
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Jedo the Jedi
Paragon in Training
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| Posted: Sat Feb 05, 2005 7:44 pm Post subject: 26 |
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| Me too. I can't think that far back, or even bend my mind to comprehend it in my own thoughts. Thanks for putting it in words L'lanmal. |
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Tahnan
Daedalian Member
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| Posted: Sat Feb 05, 2005 8:07 pm Post subject: 27 |
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Heeey--L'lanmal's second board is also sideways! What gives?
(Nice work on the analysis, too, L!) |
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CrystyB
Misunderstood Guy
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| Posted: Sat Feb 05, 2005 9:08 pm Post subject: 28 |
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i'd like to test something...
A-ha! Each second chessboard tag is switching colour placements...  |
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Tahnan
Daedalian Member
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| Posted: Sun Feb 06, 2005 6:39 am Post subject: 29 |
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| Though I see that's been fixed. Thank heavens. Now my analysis of my mini-problem is no longer stupidly wrong. I hope. |
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referee
June 21st, 2004 Member
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| Posted: Mon Feb 07, 2005 7:11 pm Post subject: 30 |
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but alternating coloring went well for multi-level (3D) chess! make that as an option, please.
_________________
Jan 21st, 2008: The pillaging continues.
Mar 4th, 2008: Rest in Peace, Gary Gygax. May your dice always roll a natural 20 wherever you are.
Be the Ultimate Ninja! Play Billy Vs. SNAKEMAN today! |
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CrystyB
Misunderstood Guy
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| Posted: Mon Feb 07, 2005 7:21 pm Post subject: 31 |
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See the thread in the News forum (or was it the Bugs thread?) - there is one, it's just not 100% debugged.
| Jeep, in IM, when i asked him for a [sideways] tag wrote: |
well, I have it in the chessvariants tag, but it doesn't work quite right
I haven't advertised it
it's a "hidden" feature until I get it working |
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