Is this position legal?

Good analysis from both. The first step in retros is usually to do this kind of analysis to look at what captures were made, and what captures you're allowed to retract from the diagram.

So now we know black's pawns on the board have taken knight, queen and "f2-pawn" (shorthand in my mind for "f2-pawn, its promoted variant or a piece which its promoted variant replaces on the board now"), while other things (pieces or other pawns) took white's rooks and c1-bishop. On the other hand, it's not obvious what white has captured, or where.

As for the issue of the last move, Colin20G has the right idea - to avoid locking the black king in you have to retract (play backwards) -1...Kc2-b3 Ka2*a1. The black king move at least can't have been a capture because as we just counted, nothing of white's can be captured on b3 by a king. But that's not the end of the story - it's still not obvious what the preceding moves were? Almost there, though.

Ok I got it now but it took me a lot of time.

PG is below. The last idea is from another puzzle shown as an introduction to retro analysis found on the web. I could have searched quite for a while to be honest.

I find this puzzle really interesting and elegant.

Exactly. I recognised it as problem 81 in the pdf you mention, which I had read and reread a few years back. It did wonders for my retro skill.

The solution I would write as -1...Kc2 -2. Ka2xN Nb3 -3. Ka1 Nbc1 -4. Ka2 Nb3xR (last 7 half-moves determined). The key to the problem is the knight uncapturing the rook on c1, giving white all the freedom needed to unravel the cage.

That pdf is really, really good to learn how to solve this type of problem. Highly recommended.

...Et si tu préfères des ressources en français, je te conseille le site d'Alain Brobecker (notamment son pdf sur les parties justificatives) et ce site pour un cours d'échecs au lycée (pertinentes sont les 10e, 15e, 20, 25e et 28e séances). Bonne lecture !

 Merci beaucoup Remellion pour ces liens!

This one stumped me when I tried to solve it playing forward instead of backwards. I saw it was easy to make ranks 1-4 like the final position except with a4 vacant. But trying to get the other pawns in the right place always left Black a move short after the three captures. I didn't realize what I did first had to be left to the end.

I thought as long as it was illegal, we can post it. Yes, I do know that Bh7 just can't go through the king and give mate lol

ok...no worries...I sometimes give newer solvers a hard time.

there at the post.

Post it

and thayer off

to a Bump start

Translation: you can apply logic to the aim of finding a move when white and black are adversaries, but can't apply logic to determining what moves must have been played based on the rules of chess.

Could this happen?:

No. In Chess, the pieces are black and white.

Well now you know they have neon in Chess.com

But really, they could get to this position. Although I think they say it would be insufficient material with these pieces. Kinda weird... but I do get why they say that. You'd have to play really bad to be checkmated like this.

Yes, it could happen. It probably would be called a draw before this positions is reached though.

This is also possible.

Last I checked, this could be a draw before the mate position with USCF rules, but not FIDE rules.

Legal?

Sure. Why not? Probably never happen in a real game, but it doesn't look impossible.