Illegal Position Contest!

Simple enough cool!

#8668

Something like this almost works:

...but there's that 3rd Black Rook, and no way to have played say, ...f3xe2 to promote it. No more missing white units.

Indeed, you did find the “release” process which I thought was a bit challenging. Well done!

Another way of thinking about the illegality is that the last move must be Nc6xBa5, but because of the intricate release process and limited pieces available for captures, the recently uncaptured black DSB must uncapture a white rook at the dark squares e1 or g1, but it can’t get there.

Here are some more positions:

#8675

Last move was Qe1xf1+

The white g-pawn made 4 captures. Black has 12 units after putting something back on f1; no spare uncaptures. Ph7 didn't capture. Thus, black must have made two captures [the two missing R's] to let it through.

f1 is a white square, so black's DSB must have been captured by the white g-pawn, on d6/e5/f4. [Not on c7, because then wP couldn't have captured the c-pawn.] This means the wP didn't pass through c6.

There is always one black major piece that cannot get back home. For example:

Or, in this case, the Q:

You can get both K and Q home, but only if you leave out Ra8 or Bf8 getting home.

Wonder if a computer program could be developed that could determine whether an inputted position is legal or not, using all the reasoning in this thread.

It's possible, but difficult. Many of the problems have long term obstacles and conflicting goals, so it would be tough for the machine to know if it is making progress, or taking an extended trip to a brick wall.

#8676

Black is apparently missing 2P and 1 N. White made 3 captures.

White is missing LSB, which was captured on f1, and N, which must have been captured on the c-file. Black made no other captures, meaning a and f pawns promoted straight down.

If only white could retract f2xe3, the position would unlock, but he must wait until black unpromotes on f1 and retracts that P to f3.

The best bet is an N promotion on f1, but it just isn't fast enough. White's g pawn can uncap an N at several places, but white runs out of pawn retractions with black's P on f2 in all tries.

Nice work with both positions! The first position was meant to be slightly harder than the second, but you still provided brilliant and concise analysis for both.

The second position seems to be just another case of white running out of tempo by one move. However, it does feature some rather interesting knight geometry: a N on f1 takes 1 move to g3, 2 moves to g4, 3 moves to g5, and 4 moves to g6. Of course, the sooner white uncaptures the bN, the more pawn tempi available, but also more moves for the bN to retract to f1.

The first one is a interesting problem in that it always comes down to one piece not getting back, and that one can be several different pieces.

I didn’t think about retracting pieces back home (apart from Ra8, which goes home once h6-h7 is retracted): I was thinking more about forward moves reaching the position, with wBg8, wPh6, bBc8 and bPs trapping the royalty. But I guess you are right - it is interesting when you consider retracting all pieces back home.

In fact, all those 4 pieces which you had mentioned in your illegality proof can return home, but only if the last move is Qe1xQf1+. This prevents a different type of piece (Bc8) from returning home.

#8681

Try - retract:

...and the Black Rooks can get home, but what is the next pawn uncapture?

* If ...e7xBf6, the bQ cannot get home.

* If b2xQc3, wBc1 cannot get home.

Yes - that is one of the tries that comes up short of legality. I would say that there are some other tries worth mentioning though.