Discuss Where Were the Kings?

[MatthewV]

Link to puzzle

[Duke Gnome]

I haven't the foggiest idea where the Kings are or how to figure it out, but it seems obvious to me that with a puzzle like this there should be a graphic near the top that you can see whilst following the discussion

[Tony Gardner]

Ah now this is a puzzle to my liking. Let's get this started.

An obvious impossibility would be for both kings to be in check, e.g. white king on a1 and black king on g7. That can't be what we're looking for of course, coz we're searching for a situation that looks impossible at first sight but isn't at closer inspection. I'll take a closer look at this in a moment, after my hang-over has passed

Anyways, I thought I'd get an early post on this one.

[groza528]

"And then the uncle repositioned the kings on a1 and g7, and the nephew said 'oops, my bad. I misremembered the position.' "

[Foggy]

I'm a bit confused as to how we're supposed to narrow down the possibilities.

With the current grids, there are 16 safe squares for the White King, and 27 safe squares for the Black King. Place the white king at H1 and black king at A8 creates a valid position.

[Tony Gardner]

Indeed. It might very well be that the inspector doesn't know the first thing about chess, and believes that white king @ h1 and black king @ a8 is an non-valid position. His nephew could then correct him.

Of course the inspector would then be extremely bored at the chess tournament they're going to

[jesus_saves]

Also, it might be important to consider who's turn it was. so one king could be in check, and it could be that color's turn.
_________________
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³⁹ Nor height, nor depth, nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord

~Romans 8:38-39

[Tony Gardner]

I think the fact that we're supposed to solve this without knowing whose turn it is, is crucial to the actual solving of the puzzle. Knowing whose turn it is opens up many more possibilities, which would make it near impossible to construct a unique solution.

[marcusI]

This is supposed to be an interresting game.
B1 and F8 would certainly make it that.

[Aalk4308]

What if the the position the inspector encountered had only one of two the kings in check, but he could prove that reaching the position requires the two kings to have at some point been in check simultaneously (perhaps they must have moved adjacent to one another). The nephew could then point out that the inspector's proof is flawed because one of the pieces on the board could be a promoted pawn.

[Guest]

Suggestions:

1. Can we use the fact that the game is interesting? Perhaps we can assume that the position does not have a forced checkmate. (I've seen a few of these puzzles before: they are known as "dead reckoning" puzzes).

2. Random observation: at least one of the two d pawns, and at least one of the two f pawns have made a capture.

[fadeblue]

We can immediately rule out some squares as not being possible under any circumstances:

White King - b7, b4, c8, c4, c3, c2, c1
Black King - e7, e5, g5, g6, h4

An interesting square for the White King is a7. At first glance it looks impossible, but Black could have promoted a pawn from b7 to create the double-check situation.

EDIT: Actually, since the game was interrupted, we can also rule out squares where a king would be in checkmate.

[Guest]

White Kc2 and Kc1 are possible, since they could be the result of a doublecheck (the Bishop moves from the c-row). But I suspect there's a quick mate in both cases.

[Guest]

Also, remember that Black's King could be keeping White's king out of check (and vice versa).

[Aalk4308]

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[Tony Gardner]

[fadeblue]

An amendment to my previous statement: some of these squares are actually valid, depending on the placement of the other king. So the only truly impossible squares are:

White King - b7, c8, c4, c3
Black King - e7, e5, g5, g6, h4

Then, if we get rid of all the checkmate positions, that also gets rid of:

White King - d8, c6, c5, a3

Not that this list does much, but I don't know a good way to approach this puzzle, and this is the only starting point I could think of.

[Aalk4308]

Some high-level but probably not useful thoughts:

Do we think all of the pieces on the board are relevant? There are so many and they are so spread out, it doesn't seem like that they could all be necessary to create an apparently impossible position.

The inspector claims that it doesn't take a grandmaster to recognize that the position is impossible. So far our thinking has been in line with his claim, as we've been looking for positions where one or both kings are in impossible checks. Are there any other type of impossibilities that would be easy to see at a glance? (Maybe they don't even involve the kings directly.)

[sodasipper]

I haven't really looked at the board yet, so I might be way off, but anyway...

The first thing that sprung to my mind with the whole "impossible position involving two kings" would have the two kings right next to each other.

Could this ever happen? I mean, the inspector would have seen it right away as impossible...

[ralphmerridew]

Given that the inspector immediately claimed the puzzle was insoluble, I think the answer is a position where there is (apparently) no last move; with the board being fairly open, that suggests to me that one king is in check. It also suggests the last move was (in roughly decreasing order of being overlooked):

- En Passant Capture (not possible only pawn that could have is d6, and there's still a BP on d5)
- Castling (not possible)
- Promotion (h8 or d1)
- Capture of piece moved immediately preceding

Related is the subject of which positions are possible without any unusual tricks. I managed to find this proof game which ends with WK on g7, BK on d7:

1. a4 a5 2. h4 h6 3. h5 g5 4. Nh3 Rh7 5. e4 Rg7 6. Nf4 Rg6 7. Bd3 d5 8. b4 Rd6 9. Ng6 Nf6 10. Nh8 Raa6 11. e5 Bd7 12. Nc3 c5 13. Ne2 Rac6 14. Ra3 Bg7 15. Ng3 g4 16. f3 gxf3 17. Nf1 Bf5 18. Be2 Bd3 19. Rc3 Bc4 20. Bd3 Bb3 21. Rxc5 Nbd7 22. Kf2 Qb8 23. b5 Ng4 24. Kg3 f5 25. b6 Rxb6 26. Rb5 Rbc6 27. Rxb7 Nf8 28. Rb5 Rc7 29. Be4 Ne3 30. dxe3 f4 31. exf4 Ne6 32. Bg6 Kd7 33. Bf7 Bf6 34. Kg4 Bh4 35. Kf5 Be1 36. Be3 Bc3 37. Bf2 Bb2 38. Bh4 Rb6 39. Bf6 Nd4 40. Kg6 Ne2 41. Kf5 Nc3 42. Rh2 Nxd1 43. Rb4 Ne3 44. Kg6 Nxg2 45. Rc4 Ne3 46. Rd4 Nd1 47. Rb4 Rd6 48. Kg7 Qxb4 49. c4 Qxc4 50. Bxe7 Qb5 51. Bf6 Qb8 52. exd6 f2

Attempting to enclose that in chess tags causes trouble; it takes over 30s to execute. And it won't accept things like Ng4+ (for check), and the like.

[Swordsman Kirby]

I think the Inspector confused which side of the board the two players were playing. From his view, he would assume he's looking at white, but in reality, black started there. Because pawns can only move forward, he was looking at a double-check with pawns, but really, it wasn't since pawns only move forward.

[Guest]

I'm getting nowhere fast with this...

Two adjacent kings are impossible so I am ruling that possibility out.

One thing I'm trying to consider is an incomplete move. For example, it black were moving UP the board, then the pawn on H6 might have just taken the H5 pawn by en passant but the white pawn had not yet been removed from the board. Similarly, the black pawn on D5 might be being taken by ep, but has not yet been removed... I've seen that same trick using castling, but castling appears impossible on this board.

Just desperate suggestions...

I've also considered seemingly impossible double checks but all can be solved by a white piece being taken and I currently have 3 different situations so none of those are unique!

[ralphmerridew]

How about: WK at a8, BK at b6. The BQ must have come from a7, b7, c8, d8, e8, f8, or g8; from any of those squares it would have still checked the king. What the inspector overlooked was that it could have been on (c,d,e,f,g)8 and captured a white piece on b8.?

[Tony Gardner]

I think that might be the best we can make of it, ralphmerridew.

The problem is, as indicated earlier, that we don't know how smart the inspector is. To me (a reasonably experienced chess player), the option of the black queen having taken a white piece on b8 is obvious, and therefore I would never have made a claim like the inspector's. The inspector might not be as experienced, though, and conclude incorrectly that the position could not have arisen.

Still, as I said, I think this could be the best we can make of it.

[Guest]

Yeah, That's what I thought of...but it has the obvious solution of taking a piece (as Tony pointed out). You could also have a pawn on A7 taking a piece on B8 and promoting to a queen. It just doesn't seem unique enough.

You can also have WK on A2, BK on C2. The bishop on B3 must have taken a white piece to get where it is.

The wording of the question implies you don't need to be a grandmaster (ruling out playing the game from scratch to see if all the pieces can get to where they are). This also suggests that he is a competent enough chess player.

Either the question isn't worded quite right or we are missing something...

[Tony Gardner]

[Guest]

Sorry about the A7 pawn thing...I'm confusing myself quite a bit.

I have toyed with the idea of the board being reversed but that would be a mean trick, especially with the squares numbered as if white are moving up the board.

I'm expecting the answer to be unique, and hopefully an 'ahhh' moment. Unfortunately, I'm still at the 'Arrrgggghhhh' stage.

I'm going to have to dig out my chess set tonight...

[Guest]

How about...

WK on E4, BK on C3

Blacks last move is pawn D5 to D7 check. White moves pawn E5 to D6 en passant, dicovering check on the black king but white has not yet removed the black pawn on D5. The inspector charges in and sees this position, declaring it illegal...but...it isn't.

[Guest]

Whoops, can't edit my mistake...

I mean black pawn D7 to D5 !!

[Tony Gardner]

Aha. Nice one. That might just be it...It seems to be unique to me.

[Guest]

Well if it is right, it will be the first one I've ever got right...not that I try too many of these puzzles...

3iff

[Guest]

I like that solution....

Also possible is WK: E4, BK: E7 and that the white pawn came from C5. Seems like an impossible situation at first glance.

[Astronaut]

That last post was mine, BTW. Why do I have to log in twice?

[3iff]

If the BK was on E7, it would already be in check from the bishop on F6. Though you are right that the pawn could have come from C5...there is no way to tell.

[Astronaut]

My bad. Eager to see if there are other suggestions, game interrupted halfway trough en passant is the best solution thus far.

[3iff]

Well yesterday I was making suggestions that black was moving up the board...and I was heavily convinced that it was unsolvable...

I think though I should have used spoilers...too late now as I only registered for the forum today.

[ralphmerridew]

The WP couldn't have come from C5; doing that would require black to end his turn in check from the bishop. On E5, the pawn would have blocked the bishop.

[3iff]

Of course...I keep looking at the board without kings in place and so checks are less obvious to spot...

[Arkive]

I just don't see how both kings could find themselves in check simulaneously, unless one of the players is in mid-move and has a piece in his hand that would obsctruct check if it were sitting on the board (such as the WQ). Assuming that possibility if false, I also think that it's unlikely that the kings are that far apart from each other (but not next to one another of course). I suspect the close proximity would likely be the only thing to stand out to the detective since he is obviously less chess-literate then his nephew who noticed what appears to be a mistake in his uncle's logic.

I really like the inverted board theory. You could place WK @ A7 with the BQ @ B8 being a recently promoted pawn from B7 (which would discover check for the BR @ C7. This would be a logical placement of the WK if it was originally @ A8 and the soon-to-be promoted pawn pushed from B6-B7 to cause check, which would force the WK back a space to A7. Where this would leave the BK is anyone's guess.

Another possibility, though far-fetched and of little use, is that one of the non-Queen black pieces is a promoted pawn that is actually another Queen. Also, food for though is the arrangement of the bishops, and even some of the pawn groupings...it forms a small pattern of sorts.