Illegal Position Contest!

Neither king can be first to reach its final square. If the white king arrives first, the black king has no path. If the black king arrives first, the white king can only arrive if the g7 pawn hasn't captured yet, but then the f8 bishop will never get to d8 since the white b-pawn will already be on c7 to let the black b-pawn move so the c8 bishop can reach e2, else the black king couldn't have arrived.

Good start, but this proof doesn't quite work. What if there was a white piece on e2 (before the kings were in place)? The white piece could then move to create a discovered check, and the black LSB could block on e2. When retracting moves, this would be "un-pinning" the black LSB. (Similarly, bNg2 and wNg4 could be un-pinned too.)

e.g. with some pieces removed

I hadn't thought of that. But if both kings are in place before the f8 bishop is released, the white e-pawn will still be at e3 to let that bishop come around, so the black knights at f1 and g2 will be in place. Then Black needs a capture at f6 and another capture by the a-pawn to promote to a black piece to be captured at c7, and has no captures left to remove the white piece that was blocking at e2.

Here is a lengthy try in which the cage is unlocked and the Kings freed. It fails because there is no way to unpromote a black N on g1. Black would have had to play ...hxg2 to get the pawn through, but I cannot retract wPh4 back to h2 with the wB on g1/h2.

The reason that occurred to me for the failure of this try is that Black must play hxg2 while leaving all of White's units on the board.

The white piece blocking at e2 doesn't have to be captured. Although it can't be wRg6 due to the pawns/pieces in the way, it could be wNg4 via un-pinning: the white knight can retract out of g4, and black could have a piece ready to retract to g4 (blocking the bQh3 check). The white piece can also be captured by black's a-pawn on its route to promotion.

Additionally, the black a-pawn doesn't have to be captured at c7 - an original (i.e. not promoted) knight/queen could be captured instead. It could be on the board now, replacing the original piece captured on c7. Also, bNg2 is not fixed in place: it could be un-pinned by a white knight, blocking wQh1 from checking the bK.

Yeah, minor detail. Will work on a better try.

Your first try is still pretty good! I didn't even notice that black's h-pawn couldn't promote due to wBh2. The only issue with this is that there are other tries (with variations) which fall just short as well but I'm sure you'll be able to find them.

I need a hint. In your valid illegality proof, how many possibilities are there that have to be ruled out?

The target is the same in all tries: retract g7xf6. This frees up the kings and the other pieces stuck in the bottom right corner. To do this, bBd8 must retract to f8 (although there is a small try with having a promoted black DSB).

To do this, we need to retract bxc7, which first requires the black LSB and b-pawn to retract back home (this is what you have noted). The LSB can only get home by being un-pinned by a white knight/rook at e2; the b-pawn can get home once a black piece un-promotes on b1 and retracts all the way to b7. The various tries come from the many ways to try and obtain these "free" white and black pieces:

• White pieces can be obtained by un-pinning wNg4, or by retracting black's axb capture. (There is also wRg6, although it cannot get out to e2.)
• Black pieces can be obtained by un-capturing on g5 and f4 (with wPg5), or by un-pinning bNg2.

How do you guys do this lol I can barely follow through the proofs with the explanations lol, let alone think up these positions!

I think being hard to explain is what makes an illegal position a good one. daStrwbrry has made some of the best.

No I agree, but it's just so impressive. How do you guys make them so flawlessly despite needing 5 interacting aspects of the position that together make it impossible in the most subtle way..

Yeah, the composers on this thread are really really smart.

really just a map of everywhere the knight can go in three moves

 :wp :wp :wp :wp :wp :wp :wp :wp :wp bc there cant be 9 pawns

*But nobody came

lol