legal AND illegal positions

You mean, after white played a4, black was the last to move. Just because it's a retrograde analysis doesn't make time go backwards. The position is listed as white to move (not to mention white is in check), so obviously the last move made was by black. Before black's last move, white had to have made a move. I don't think anyone has been confused about this, yet you keep "correcting" us for some reason.

White is in check from the knight on h5. Therefore black must have played the knight to h5 on his last move. I don't see any way around that. On the otherhand, it also isn't particularly important to the rest of the analysis.

Now, about white's last move (which was obviously before black's last move). Let's answer the question: could it have been a king move? The king would have to move from f8 or f7. The king could not have been on f7 with the black bishop on g8 and black knight on h8 -- there's no way for black to give this double check. The king could not have been on f8 and triple checked by the queen on d6 and the knights on h7 and g6. Therefore, there are no squares for the white king to have come from on white's last move.

White's last move must have been either a4 or b3.

What I pointed out in my first post is that it takes black a lot of promotions and therefore a lot of captures to get to this position. There are a couple different ways to go about it, but the upshot is that you can't move both the a and b pawn because one of these needs to be held in reserve. 

When I said, "before White played a4," I was referring to one of the two positions below:

In these positions, it is White to move (he's about to play a4), so Black was the last to move, right?

 Getting back to the final position (where White is in checkmate), there IS another possible last move that Black could have made, and it IS significant to the analysis once you find it. There's also Position 2 (from the original puzzle in post #116) to consider... although any hour now einstein will have the whole thing solved and post the full analysis here, so I'm not even sure why I keep bothering to point these things out

Loomis, that game fails to reach either of the two positions from the puzzle - check post #116 again... or was that just a joke? 

Eh, I realized right after posting it the queen was on the wrong square. But the position of the queen isn't so important, so I left it. I'll go back and fix it just to make you happy.

Omg, either you're really getting a kick out of this, or you still haven't checked post #116. Einstein_69101, where are you? :P jk

No, I actually did overlook the knight on g1. Oops.

I was actually trying to demonstrate that there aren't enough captures available. I was trying the line where white promotes twice by capturing on a2, but since black has made no pawn moves other than a3, this took both knights to accomplish.

I think I'll go back to my original conclusion that there simply aren't enough captures.

 It seems you're getting close to solving it, now. Looking at that "proof game" more carefully, I noticed that you had found the other possibility for Black's last move: N4xh5# (instead of N4h5#). But Position 2 has not yet been addressed - at all. The original puzzle's question involves the legality of both positions.

You can stop bolding and italicizing that point. I'm not missing it.

I probably should have mentioned that regardless of what black played before white's a4 move, white didn't have any other legal move.  Black has made eight captures already so this means that when black checkmates white, then white didn't have another piece to move.

There is the possibility that black's b-pawn promotes with just one capture (bxa3) and promotes on the a1 square after white has played a4.  In this case, black can promote six times with just seven captures (five captures by the a-, b-, c- and d-pawns, one capture on f1 and another to capture white's h-pawn.)  This requires that black plays axb2 before white plays a4.  But this also means that white has to play a4 and b3 early.  And the only possible move that white could have made was Rh5+ right before black plays N4xh5#.  The continuation of the proof is similiar to the proof for post #114.

Position 2 is nearly identical to Position 1.  The difference is that the rook is on f5 instead of c4, the black knight is on f4 instead of h5 and it is black's turn to move.  This means that white just made a move.  White didn't just move his king because of reasons stated earlier.  The white knight is trapped, and white's last move was not b3.  Black needs white to play b3 so his c-pawn can promote with just one capture.  This means that white has just played a4.  And black is required to have a minimum capture count of eight as shown from the analysis of Position 1.  It is impossible that white's a-pawn has moved from a2 to a4 because white had to play a3 early so black can get a promotion on a1 and meet the maximum of eight captures.  Regardless of what black played before white played a4, white had no previous legal move.

Edit: I should say that black can get all of his promotions with just seven captures in Position 2, but this requires white to play a4 and b3 early.

I say they are both illegal.

Legal or Illegal?

Legal or Illegal?

Hmm looks like a Bongcloud variation to me...

 Now THERE'S the analysis I've been looking for! There's a problem, though: your final answer (which corresponds to choice "D" from post #116) is incorrect :(  I'm not going to give the correct answer, though; I'm sure you can figure it out (or maybe someone else will).

I highlighted two "confusing" sentences. For one thing, in Position 2 there is no White rook - how could Black's final move be "N4xh5#, capturing a rook" ? It's probably unimportant, but... I'm just curious.

Now, in the analysis for post #114, you pointed out that a "last-minute" capture (one of the 7 captures, and 5 pawn captures, that Black must have made), hxg4, could have preceded White's Rh5+ : but refuted it with this reasoning:

1. The only White pieces that could have legally moved to g4 were a knight or a bishop.

2. Since White's light-square bishop can't have escaped from f1, the bishop on g4 would need to be a promoted pawn. However, because White hasn't made any captures (all 16 Black pieces remain), neither of White's missing pawns could have promoted without making it impossible for Black to promote 6 pawns with only 5 captures (in addition to N4xh5#).

3. Since White still has two knights, a knight on g4 would necessitate a pawn promotion by White (which is impossible, as explained before). 

Does the above logic hold up for the new positions?  ;)   Actually, I recommend rechecking ALL previous analysis - are there any conceivable loopholes?

Okay, so I keep trying to make an illegal version of this puzzle.

Oh, here it is.

Legal. Though inputting this really made my comp lag.

What about this:

Legal or illegal?

Now that I look back at this problem, it's kind of easy.