Illegal Position Contest!

Funnily enough, there is another case, and this one makes the position legal. We all overlooked this possibility:

Probably an easy fix with wPd4 to d3 anyways

Overlooked, nothing ...! These problems aren't designed to have solutions. 😂

Ah well, let's just all pretend the pawn was on d3 this entire time 😅

(I've actually had a position in the past with this exact same issue of the double move from the pawn allowing for a capture instead of a pawn advance, so I really should've remembered the geometry...)

Unfortunately I feel like Pd3 makes the position look a little strange. How about a very strange position? This one is more annoying than it is actually difficult:

plus Hyra#1 brawl stars player

It seems that the issue is with getting that second black LSB, rather than the retraction sequence of checks, which can be resolved. White is missing just Rh1: two of the white pawns promoted to DSBs and the last pawn promoted to a rook. A black pawn capture must be made for a LSB promotion on b1 or d1 (f1/h1 are blocked) but the missing white rook cannot get captured over there.

Yes, that's it! I thought it would be funny to try and disguise the illegality as having something to do with retractions; although, I'm pretty sure it can be resolved in only 2 retractions.

Do you think you can change the position to make the retractions illegal instead? I think the farthest it can extend to is unpromotion of Bh8.

Move 1 is pawn takes king 👑 😂

Seems there are several ways the short term retractions can go. One is:

I think I've managed to make all possible retractions illegal. There was quite a few retraction sequences possible in the original position, so I've had to change a few pieces, and I added some pieces as well to prevent un-captures.

That looks pretty good! I haven't looked at it too carefully, but I think it should be solid. It seems like the required captures make it so that there aren't enough pieces for extra shields to be used, so retracting discovered checks should be the only option.

Do you think the position could still work if wQ is moved to d1 and Bd3 and Qh3 are swapped? My initial idea was for the first black knight retraction to stop the retraction of white's rook, so when the retractions all "wrap around" it would turn out that the first retraction makes the last one impossible. (At some point I got tired of figuring out how the pieces should be placed and conveniently I ended up with a position that was illegal due to the color of the bishop promotion square again, so I just went with that (: )

This is such a fascinating thread. Would be even more interesting to design a computer program that could detect whether a position is illegal or not using these advanced retraction algorithms + other retrograde analysis/mathematical parameters!

You can't swap Bd3 and Qh3 since that would allow -1...Nd1-e3+ -2. Nf2-e4+ Qe3-d3+ -3. Nd3-f2+. But it is possible to make the knight interfere with the white rook retraction, after moving a few more pieces:

That's a really nice way to deal with it! Either the knight stops the wRd2 or the bBd3, and there still aren't enough pieces to act as shields.

Looks like you made it to 7 retractions now; do you think you can make a position with more retractions until an illegality?

Actually I think that would be easily possible with a "not enough waiting moves" position. What about a position with more than 7 retracted discoveries?

I've finally done it! This position is quite different from the original but I believe it goes up to 9 retractions (all checks, nearly all discovered checks) until no more can be done. This took a long time to create due to the interferences, limited pieces to work with, and sneaky retractions which resolve the position. Let me know if you encounter any issues.

I haven't really checked over the position yet, but is this the intended retraction sequence?

Yes, this is the main retraction sequence, which lasts the longest. There are other shorter variations but all of them also fail eventually.

Determining the possible pawn trajectories and captures is an arduous task, but it prevents uncaptures and certain retractions later on (e.g. d7-d8=R+, f6xg5+).