Legal position? (Part 3)

This one's quite a bit harder than last time, so good luck!

It took me quite a while to see why this would plausibly be an impossible position, but I finally realized that the white king seems like it might have trouble reaching its current location. Time to see if there's a way to bypass the defended squares...

EDIT: Oh, okay, I'm being dumb...the main thing is actually the "Black to move" bit. There doesn't seem to be any square any of White's pieces could have come from...the two pawns further forward on the g and h files could only be the e and f pawns originally, indicating that the pawn on the e-file is the original d-pawn. But if White's last move was dxe3, then it seems the king could have problems leaving the vicinity of its starting square...this merits further thought.

RE-EDIT: Me being dumb again. dxe3 was not a legal last move.

I'll go with no, becouse white last move would have benn e3 or fxe3 but f and e pawns are nedeed on the g and h file.

 White's last move was not necessarily e3 or fxe3.

Okay, the answer seems to be that it's illegal. Here's how my logic goes:

- White only has a few possibilities for the previous move, namely (a) moving the king from a8 or b8 to a7; or (b) moving the pawn from e2 or f2 to e3.

For option (a):

- If the king was on a8 or b8 on the previous move, then it was in check from the rook. Since there is a pawn on f7, the rook could not have moved onto the eight rank to give check previously, nor is there any piece that could have moved away to deliver discovered check. Hence, the last Black move must have been 0-0+.

- If the last Black move was 0-0+, then the Black king must not have moved from e8 since the start. Given that on e8 it prevents the White king from entering d7, e7, and e8, there is no way for the White king to reach a7 without the Black king having moved before (since the b and c pawns are still on their initial locations, forming a barrier from a6 to d6).

- Therefore, option (a) is impossible.

For option (b):

- The two pawns further forward on the g and h files could only have been the e and f pawns originally. Hence, the pawn on e3 could not have come from either e2 or f2.

- Therefore, option (b) is impossible.

Conclusion: The position is illegal. Did I miss anything?

Very good analysis, Tyzebug! However, there IS, in fact, something you missed.

I can't say I disagree with Tyzebug... The only iffy thing is the king but his explanation seems dead on. All other pieces seem very easily and logically accounted for as not having moved last turn.

black had a night on c8 so Na7+ Kxa7!!!!!!

you made me mad!

 Absolutely right!!!! But there's still more ;)

black cuold have even had a bishop on b8 with the white king in a8 that's equal, Ba7+ Kxa7

 The only problem is that, according to Tyzebug's analysis, the queen and rook sitting on h1 and g1 serve absolutely no purpose. Chry3841's point is where these two pieces come in.

Oooh, very slick. Can't believe I missed that discovered check possibility...was being quite boneheaded there. As for whether it's a knight or bishop...hmm, probably something to do with whether it's possible to promote a pawn to a third knight given the number of pieces on the board...needs further thinking. To metagame it a little, the bishop option seems more likely since if it was a knight that delivered discovered check, there were two squares the king could have come from, and that's less elegant. :P Of course, there's also the possibility both are illegal.

EDIT: Okay, some quick analysis suggests it can't be a knight because it could only have been promoted from the g-pawn, since the h-pawn is needed for White's f-pawn to reach the h-file; whereas the a-pawn is needed to get to d2 since the g-pawn can't bypass the white pawn on e3 to get to d2. But the g-pawn needs at least one capture to promote, whereas three captures are used up getting the a-pawn to d2. Since there are only three white pieces missing...yeah. Now time to see if it's possible to find a proof game for the bishop...

MORE EDIT: Oh, so that's the crux of the problem. It's not possible to be a bishop either, because if that's the case the position before this would be

But the fun thing about this is that there seems to be no possible move for White before this position either. So there goes the bishop option too...(and while the knight option avoids this problem by giving the white king space to run around between a8 and b8; it runs into the aforementioned problem of having no pawn to be promoted from. Incidentally, slight addition to the previous analysis: while I think the original line of thought was legit, here's a better and easier-to-understand one. For White to have those pawns on e3, g4 and h4, five captures are needed, and exactly five Black pieces are missing. So there are no pawns that could have promoted to a knight). Does that cover it?

 You're refutation of the bishop possibility is dead-on, but unless I'm going blind, Black has only 10 pieces, so 6 captures have been made, not just 5. Also, why couldn't Black's d2 pawn have originally been his d, e, or g-pawn (with the a-pawn promoting to a knight)?

yes it could be if the g pawn became the e one and the a promoted taking on b2.

Whoops, was counting the pieces on the wrong diagram (the one still with the bishop). Your point about the d2 pawn is interesting...I assumed that the d and e pawns on the fifth rank were the original d and e pawns, but now that I look at it it seems like a risky assumption to make. Will think about it later.

 Ah, but did you count up the number of White pieces captured in that situation?

Judging by the number of corrections I've had to make, I should probably think my solutions through more before posting them, but meh. Here's my thoughts on the knight possibility (it's actually the same thing as what I originally mentioned, only this time I tried to construct a rigorous chain of logic):

- There were 6 black pieces captured, and 3 white pieces captured. But if the previous move was discovered check from a knight, then only 5 black pieces were captured at that point.

- The white pawns on e3, g4 and h4 require 5 captures to reach that position. Hence, the 5 black pieces that were captured must have been on e3, f3, g3, g4 and h4.

- Black's a-pawn could not have been one of these captures since it cannot reach any of those squares with only 3 white pieces captured. Therefore, the a-pawn is still alive and kicking somewhere on the board.

- The only pawn currently on the board that could have been the original a-pawn is the d2 pawn (even with unlimited captures, it can't reach any of the other pawns' locations). To get there, it would have used up all 3 white captured pieces.

- Therefore, all other black pawns had to stay on their original files. As such, the only pawns that could have promoted are the g- and h-pawns.

- However, with White's g- and h-pawns still in place, and all 3 captures used up by the a-pawn, there is no way for either the g- or h-pawn to promote. Hence, the knight discovered check is also not possible.

How does this one fare?

What if the a-pawn was the knight that got taken by the king on a7?

-.- And this is why I really need to check my solutions more. Luckily, this bit looks simple enough: If the d2-pawn was the original g-pawn, it would need 3 captures (4 if it was the original h-pawn, making that option right out...insert obligatory Holy Hand Grenade reference here) to get there; hence leaving the a-pawn with no way to get past White's a-pawn to promote.

the black a pawn could have eat white b pawn