Originally posted by Jirakon+wKc4, bKc6 is legal (how?).
Ok, that one ended up worse than I expected (I actually had a thrid solution; see if you can find it). This puzzle started much differently. I guess in all my messing with it, it got cooked. Here's what it started as:
Black 1
[fen]7Q/6Q1/5Q2/4Q3/3Q4/2Q5/1Q6/Q7[/fen]
White 9
Again, the last move did not involve a capture. The puzzle is still to pl ...[text shortened]... ition is legal, or else prove that the position is illegal regardless of the kings' positions.
Well, let's see: White's last move was with the queen to f6, which did not involve a capture. Hence Black's last move was with his king. No matter where the black king came from, he must have been in imaginary check (either from the white king, or from two different white queens). Could you go back several moves?
Originally posted by Jirakon-1.Qf6+ Kb6xPc6!! -2.b5xc6e.p.+ c7-c5 -3.Qd4+
Well, let's see: White's last move was with the queen to f6, which did not involve a capture. Hence Black's last move was with his king. No matter where the black king came from, he must have been in imaginary check (either from the white king, or from two different white queens). Could you go back several moves?
Edit: Smullyan fans should know this trick!
R. Smullyan
Die Schachgeheimnisse des Kalifen 1981
Where is the wK?
Answer: c3. Retract -1.Kb3xPc3+!! b4xc3e.p.+ -2.c2-c4 Bd5+
Wow. I don't yet have a solution for your editted puzzle, but I'm just going to go ahead and post my next puzzle, for which your idea of an illegal cluster was the inspiration. I define a reverse legal cluster about x0 as a legal position in which if any piece were added to the vacant square x0, the position would be illegal. The "reverse" comes from the fact that a piece is added, not removed.
Black 13
White 12
Add 5 white pawns, 2 white rooks, 3 black bishops, 3 black pawns, and 1 black knight to make the position a reverse legal cluster about some square.
Originally posted by JirakonAdd bNg2 and some other piece (not a bB) on e3. Already, I can fulfill the stipulation: No piece can be added on e1 (last move is ...Ne1-g2+). The rest of the pieces are superfluous.
Wow. I don't yet have a solution for your editted puzzle, but I'm just going to go ahead and post my next puzzle, for which your idea of an illegal cluster was the inspiration. I define a reverse legal cluster about x0 as a legal position in which if any piece were added to the vacant square x0, the position would be illegal. The "reverse" comes from ...[text shortened]... ck pawns, and 1 black knight to make the position a reverse legal cluster about some square.
With this kind of stipulation, it will be difficult to prevent cooks involving a checking piece that must have come from a certain square.
Wait a minute! I was just going to give up the problem and call it cooked, when I realized I could make a slight modification which may actually present a challenge. (then again, you've cooked just about every other one I've presented, but we'll see)
Black 12
White 12
It is given that neither queen has ever been on a square with a different color from her starting square. Now the puzzle is to add 5 white pawns, 2 white rooks, 3 black bishops, and 4 black pawns to make the position a reverse legal cluster about two different squares (meaning that there are two squares that cannot legally be occupied).
Sorry if I can't present any significant challenge for you, but it looks like I'm the only trying, so I'll do my best.
Originally posted by JirakonWell, this one was more challenging.
Wait a minute! I was just going to give up the problem and call it cooked, when I realized I could make a slight modification which may actually present a challenge. (then again, you've cooked just about every other one I've presented, but we'll see)
Black 12
[fen]8/4k3/8/8/r2p1K1n/6p1/P6P/1N4N1[/fen]
White 12
It is given that neither queen has e significant challenge for you, but it looks like I'm the only trying, so I'll do my best.
I tried some elaborate unchecking schemes, but the awkward position of wK relative to bK limits the possibilities. Also, the pieces to be placed have been carefully selected to avoid any "faraway" double-checks.
Then, over dinner, it hit me. I borrowed a recipe from your cookbook: the "too many captures" idea.
White and Black made 4 P captures each, so no more units can be placed on the board.
Originally posted by JirakonHow about this:
Awww...I knew this would happen. How about this then: Make it a reverse legal cluster about exactly two squares. Hopefully that will get rid of any more cooks. (only time will tell)
Last move was -1.fxe8R+. White pawns captured all 4 missing Black units. wBc1 died @ home; wQ and Bf1 died on light squares. e5 and c7 can't be legally occupied - only a wR is left to place, but that results in an imaginary check.
wBc1 died @ home; wQ and Bf1 died on light squares
How do you know any of them were even captured? What if one of them is still on the board, and the other rook was actually captured? Anyway, even if you knew that it must have been a white rook, wouldn't d7, e6, and f7 result in imaginary checks as well?
Originally posted by JirakonAck! I didn't do a good job presenting my solution. Sorry...
wBc1 died @ home; wQ and Bf1 died on light squares
How do you know any of them were even captured? What if one of them is still on the board, and the other rook was actually captured? Anyway, even if you knew that it must have been a white rook, wouldn't d7, e6, and f7 result in imaginary checks as well?
Let's try another explanation.
I know that wQ and Bf1 cannot travel on dark squares; that is all that matters in my solution.
I can legally place a wB on d7, e6 or f7, so those squares are 'safe' under your stipulation. However, it's not possible to place a wB or wQ on e5 or c7 (because they are dark squares, Bc1 died at home, and there are no wP left to promote). The only available piece is a wR, which is clearly illegal.
Originally posted by Jirakon[double post]
wBc1 died @ home; wQ and Bf1 died on light squares
How do you know any of them were even captured? What if one of them is still on the board, and the other rook was actually captured? Anyway, even if you knew that it must have been a white rook, wouldn't d7, e6, and f7 result in imaginary checks as well?
There's still one minor problem: you've again made a position in which no piece can be added anywhere on the board (except f7). How does black have two bishops on black squares? A pawn must have promoted on either e1 or g1 (since it couldn't get to a1 and couldn't escape c1). That requires a minimum of two captures. Add that to the capture made by one of the pawns on the g-file, and the missing bishop from c1, and that makes four captures, so white can't have any more pieces on the board either (not even a rook). f7 is an exception because a black knight on f7 means that white may not have just made a capture, and the rook on e8 may be original, which means that white only made three pawn captures and the extra knight is possible. Well, if the question were to make a reverse legal cluster on all squares but one, then you've got it.