Illegal Position Contest!

Here's an illegal position that you might think ought to be legal, since it would be legal with the h3 pawn on h4. Why is it illegal?

I was going to post a shorter explanation for confirmation, but I'll just get started on my longer one right now. Am I correct?

TLDR; no possible shields exist for bBg1 to be set up. Moving wPh3 to h4 allows for black's king to act as this shield.

• The black pawn on c2 must be the black h-pawn, or else the black LSB will not be able to reach g8. This means black requires 5 captures to reach c2.
• White's LSB and kingside rook were sacrificed to set up bPc2. Both of these pieces require wPg2 to get out of the way. Black sacrifices a knight on h3 for this to happen. By this point, the white pawn is already on h3 and black is missing a knight.
• The c2 pawn must have been set up after white's king reaches a1, or else white's king is cut off.
• Since wPd2 can only be played after the c2 pawn is set up, the white DSB could not have gotten out before that, meaning that white's queenside rook couldn't have gotten out, so it must have been captured at home to make room for white's king.
• This means that one of white's pieces wasn't captured (DSB), five were sacrificed to set up black's pawn, and one was captured at home, so by the time bPc2 has been played, white's only piece is the DSB.
• bPb7 can only be played after the white DSB reaches a7, which allows for the black LSB to get out. bPg6 can only be played after the black LSB reaches h7 (from which it can move to g8), which would allow the black DSB to be released.
• This means that by the time black's DSB gets out, white's king is already stuck on the first rank and white has no pieces besides the white DSB, which is stuck behind black's pawns.
• Black's bishop cannot reach the first rank with wPf2, so black must sacrifice their remaining knight on e3 so that wPf2 moves out of the way.
• At this point, neither side has any knights, so the only pieces that could possibly block a rook check are bishops. White's DSB and black's LSB are both stuck behind black's pawns, leaving black's DSB as the only option.
• A shield is needed because white's king is stuck on the first rank, and black's rook must reach h1 without checkmating white.
• Black's rook cannot reach h1 if black's bishop is on g1, so black's bishop can only act as a shield on e1. Unfortunately, with black's rook on the back rank, black's bishop cannot ever leave the back rank without causing a discovered check, so it can never leave e1 and move to g1. Therefore, the position is not legal.
• If the h3 pawn were moved to h4, black's king can now get behind white's pawns and act as the shield, freeing black's bishop to go to g1.

Edit: improved readability

Giving me a headache lol

Yes, you are correct. Here's a proof game for the legal position with the h3 pawn on h4.

Do you mean in the TLDR that the h3 pawn prevents black's king from acting as a shield?

Oh I think I get the idea, really good!

Oops. It should say that moving wPh3 allows the black king to act as the shield. The issue has been resolved.

Here's a position that's related to my previous position, but the pawns don't keep the black king from reaching the first rank, and I can even post a proof game for this position. But it is still an illegal position. Why do you suppose that is?

Without doing anything I assume 50 move role

Now you just need to explain why the position can't be reached in 50 moves or less after the last capture or pawn move.

Except it's not illegal to exceed 50 moves without a pawn move or capture. Whether it's illegal to exceed 75 moves depends on which rules you assume (FIDE basic rules v competition rules).

But the latter is also not illegal under the local chess variant @n9531l1 usually assumes.

But I've decided to call a composed position illegal if it requires moves after the game has ended.

Should rules for over-the-board chess be applied to a composed problem, rather than the rules found in the Codex for Chess Composition? (See what Article 17 of the Codex says about retro-problems, which include proof game problems.)

50 move rule shouldn't apply to endgame studies, long puzzles, or tablebases. It's more of a tournament regulation rule rather than a solid rule of the game, such as can't castle through check. What's funny is that games which have actually ended, such as this one:

The site doesn't declare as ended, even though it is a draw as no side can ever checkmate the other! LOL

Nh3 d6 Ng1 d5

50 move rule shouldn't exist at all in any of that. It should only be used in OTB tournaments, preferably at least 100 moves.

Possibly so. The only problem is it does exist in many sets of rules. But as I said earlier it has very little relevance to legality. The 75 move rule under FIDE competition rules, however, does.

No move limit should exist for anything, other than OTB tournament games. Whether that should be 50, 100, or 75 I don't know.

I interpret the Codex article to mean that the 50-move rule does apply to retro-problems. In that case, it applies to every retro-problem unless stipulated otherwise, including #7721.

Have you tried to see how many moves #7721 requires?