Discuss Decimate here

[MatthewV]

link to puzzle



Chess tags may be used to create chess boards on the forums. Because this puzzle does not need anything beyond piece placement, that is all I will cover. (For details, see Welcome to Visitor Games)

Typing [chessboard]8/8/8/5k2/3K4/8/8/8[/chessboard] will create the starting position of this puzzle. To add pieces, use capital letters for white pieces and lower case letters for black. Rook, kNight, Bishop, Queen, King, Pawn are the letter codes. Numbers represent blank spaces between pieces or left in the row.
For example, [chessboard]Q7/1B6/2R5/5k2/3K4/8/6P1/7N[/chessboard] looks like...

[Rinn]

Fan of the site. First time posting.
Ok. think i got it. Going to take a crack at it.


Queen=G8
Bishop=G5
Rook=G7
Pawn=H3

I am thinking the Rook is guarding G6 and the Bishop at G5.
The Queen is only guarding E6 because it is blocked by the Rook.
The Bishop has F4 and F6.
The King has E4 and E5.
And the pawn has the last at G4.


Anyone agree?

[Courk]

[hijack] Welcome to the site! [/hijack]

[Griffin]

Rinn -- where is Blanc's knight?

[Rinn]

[Aalk4308]

I've been looking at this since it was posted and have made some observations I hope are useful. Please check my reasoning before relying on it: I have a habit of faulty logic in chess problems!

The white king is already guarding e4 and e5. This leaves six squares to be guarded by the five remaining white pieces. So, one of the remaining pieces must guard two squares and the rest exactly one each.

At least one white piece occupies one of the eight squares around the black king. If not, then the white rook would have to guard three squares, which is impossible per the above. With a white piece in one of the eight squares, the rook could be positioned to guard the required one or two squares.

What piece(s) could occupy one of the squares around the black king?
Queen: Obviously impossible, since the black king would be in check.
Rook: It would have to be on either e6, g4, or g6. Moreover, there would have to be white pieces on the adjacent two black squares to prevent the rook from guarding more than two squares. One of those two pieces would be a knight, bishop, or queen, which would also be attacking at least two squares, which is impossible since the rook is already doing so.
Bishop: It would have to be on g5 and the rook would have to be on h5. (If the bishop were on f4 or f6, it would guard e5, which the king is already guarding. If it were on e5, the rook could not utilize the bishop to prevent it from attacking three squares, since doing so would require it to guard e5, which the king is already guarding. In that case, there must be a white piece on e6, g4, or g6 to allow the rook to guard just that one square. It can't be the knight or the queen because they would have to guard more than two squares. If a pawn, it would have to be on g5, with the rook on h5. This leaves the knight and queen to guard e6, g4, and g6, which doesn't yield a solution.) Now, the queen, knight, and pawn must each guard one of e6, g4, and g6 and, obviously, none of the other squares. The only way for g6 to be guarded is with the knight on h8. The pawn must be on d5 or h3, and the queen appropriately placed to guard the last square. Neither possibility solves the problem. Therefore, the bishop is not on one of the eight squares around the king.
Knight: It could be on either e6 or f4. If e4 or e5, another piece would have to be next to the black king. It could only be a pawn on g5 and the rook on h5. So the knight can't be on e4, else the pawn would be guarded twice. Moreover, there is no way to guard f4 with the queen and bishop without guarding other squares.
Pawn: Obviously it can only be on e5, f4, or g5.

So, the main conclusion so far: there must be a white piece in one of the eight squares around the black king, and it could either be a knight on e6 or f4, or a pawn on e5, f4, or g5, or a combination.

One other thought: To generate the 10 possible one-move mates, I thought many of them (if not all) might be the result of a discovered check. The piece moving out of the way would have many possible moves, each of which is mate.

[Talzor]

Nice observations Aalk4308, Although I'm not sure I agree with your initial assessment:

[Amb]

"and no square around the black King was guarded more than once"

The white king is currently guarding two squares, so a piece must sit on one of those squares.

[Samadhi]

amb: You've got it backwards. It's okay for the king to guard two squares, but the king and another piece can't guard the same square.
_________________
And he lived happily ever after. Except for the dieing at the end and the heartbreak in between.

[Aalk4308]

I see what you mean Talzor. I definitely agree with the point about pawn positioning. In your example, the pawn on f6 is participating in delivering the "perfect" stalemate even if it isn't guarding a square itself. I'm not sure if I agree with your second idea though. I think saying all pieces participate in a stalemate means they are involved at the point in time of the stalemate, not at some point before in helping deliver it. For example, if a series of checks forced the black king to move to a square where it is ultimately stalemated, would it be right to say that any of the white pieces that delivered a check participated in the stalemate, even if it doesn't guard squares around the king at the stalemate itself? I'm not sure.

Also, I see you tried the discovered check idea in your example. I don't think there are any mates with the knight though. If you move the knight, f4 and g5 would no longer be guarded, so the check from the bishop would not be mate. This illustrates a general problem with the discovered mate idea: if the blocking piece is also guarding squares, moving it to discover check would also mean those squares are no longer guarded (and they can't be guarded by anything else because of the one square one guard requirement). Can this be worked around?

[fadeblue]

Aalk4308: Talzor's "pre-stalemate" board has f4 and g5 guarded by the Queen.

[Aalk4308]

Thanks fadeblue, I'm an idiot, mixed up the two diagrams!

[noah*]

Q: C-4
N: H-3
B: E-8
R: G-1
P: G-5

Now there arent ten ways to win on any previous move, but other than that, I think this arrangement satisfies your requirements.

[Rohit*]

This is the first time i am using this site.
Not familier much with chess but...i guess this might be the final setup :

[Rohit*]

[Talzor]

[casinopete]

Talzor: looks like you have 12 mates, there: 6N+6Q.
fnord.

[Talzor]

[Oscar]

Think I've got it...

Final stalemate setup:

[Talzor]

Nice work, but Bd7 is not a mate as it leaves g6 unguarded. However if you do indeed "invert" the rock and bishop's position to:

[Aalk4308]

I think that's close Oscar! The only issue I see is that Bd7 isn't mate, because the black king could move to g6, right? So we only have 9 mates instead of 10. Could you show what happens when you switch the positions of the rook and bishop like you suggest? (I tried it quickly but didn't get it, and now I'm late for work!)

[Oscar]

No - since the bishop can give mate on G4 and C2.
Dang! So close...

[Antrax]

I count 11 mates in Talzor's position:
Rf8, Nh4, Ne3, Qc2, Qd3, Qe4, Qf4, Qg4, Qc8, Bc2, Bg4.
_________________
After years of disappointment with get rich quick schemes, I know I'm gonna get rich with this scheme. And quick!

[Talzor]

[groza528]

I might point out that technically, the phrasing is "no less than ten mates," which would not preclude a solution with more. The next sentence ("all ten") might, though

[Raven*]

I'm not all that familiar with chess--I know the basic moves for each piece, and that's about it, lol. But I have a dumb question... Is there a rule that white must play from the "bottom" of the board as it looks in the picture?
I know the pawn is only able to move forward, but if white plays from the top, obviously it would change which squares that the pawn guards from its position. It might not even matter to the puzzle solution, but I'm curious as to the "standard."

And, from reading y'all's previous posts, is this the solution, then? :



with this as the pre-stalemate board? :





???
It looks right to me... you guys are smart!


--Raven
P.S. How long before the solutions to "unsolved" puzzles are usually posted? And when will there be a new puzzle up to solve? lol

[Raven*]

[MatthewV]

Sometimes the solutions get posted as the next one go up. But please don't be too demanding

I do believe there are exactly ten mate positions in the correct final answer.

White is always coming from the bottom of the screen also. We already had a "mate in one" puzzle that relied on giving a side view of the board.

[marcusI]

For "white on the bottom", when the number and letter system is used
there is a standard.

Per Wikipedia: http://en.wikipedia.org/wiki/Algebraic_chess_notation

[dowser]

The puzzle says that we have enough information to reconstruct the position.

The board that Talzor posted looks good, and satisfies the mate and guarded squares requirements, but couldn't white's rook sit on either g7 or g8? And if so, this can't be the answer since we don't have enough information to fully reconstruct the position.

[Samadhi]

Neither is the intended solution, but I don't know what (or if) there is anything wrong with them.
_________________
And he lived happily ever after. Except for the dieing at the end and the heartbreak in between.

[Guest*]

[Aalk4308]

[Mobius99191*]

I have to agree with Samadhi regarding Talzor's answer. And then I'll add my own spin...
I think this (with permutations involving the Bishop and Rook) satisfies the constrains as a 'pre-stalemate' setup:

[guest*]

But that type of setup isn't unique because the bishop could be on d1 (mate with c2 and g4)

It does satisify all the requirements as far as I can tell.

[Kutti]

In the presented solution (the first one) Qf3 is not mate, because the field e6 is not guarded.

Kutti

[Talzor]

Qf3 should probably have been Qd7.

[ralphmerridew]

I was just looking back over this and noticed a problem: in the official answer, E4 is guarded by WK and WQ; Mobius99191's solution has more multiply-guarded squares.

[Talzor]

The pictures on the Solution page show the board before the stalemate move. After the move (either the queen or the king, depending on which solution) the squares are only guarded once.