Retro Challenge #2

I'm not quite sure you understand the point of the challenge, k-scope.  It isn't to simply create a position where an underpromotion to a knight could have occurred (and no knights are on the board and neither king is in check), but to create a position where it can be proven that such an underpromotion has occurred.  In other words, there is no other way to get to that position in a legal game.  With your first position (and probably with your second, but I didn't confirm it to myself before writing this post), it is possible to get to that position without any promotion occurring, much less an underpromotion to a knight.


In Shoopi's position from post #6, it can be proven that an underpromotion to a knight has occurred.


First, we take note of missing pieces:
White is missing only two knights.
Black is missing a pawn and two knights

Now, take note of the pawn on a5.  It had to have come from d2 (since the a2, b2, and c2 pawns are all still on their original squares).  Since black is missing three pieces, they had to have been captured on c3, b4, and a5.

The two knights could easily have been captured on any of those squares, but the missing pawn is from f7.  Since white is only missing two pieces, that pawn could not have captured all the way over to the c-file.  Thus, it must have promoted.

In order to promote, given white's pawn formation, it had to have made at least one capture.  Because of this, the pawns on a6 and b6 could not have cross-captured (axb6 and bxa6).  I don't think this is vital to the current proof, but it is a common feature in retro problems so I figured I'd mention it, anyway.

So now we know that the black pawn promoted, but how do we prove it promoted to a knight?

Well, notice that it is black's turn to move.  What was white's most recent move?

It couldn't have been the pawn on a5, because that pawn had to come from b4 which is currently occupied by a black rook.  Similarly, the bishop on a3 couldn't have been the most recent move.  None of the pawns on the second rank have moved, the rook on b1 and queen couldn't have moved from anywhere.

The pawns on e5 and h4 couldn't have moved because we've accounted for all captures and there is a piece on the squares those pawns would have come from.  The king couldn't have moved from h1 because there is no way for black to have created that check (the rook couldn't have moved to h2 on the prior move).  Finally, the bishop on c8 couldn't have moved there because of a phantom check on b7 - that is, the black king would have been in check before white moved the bishop, which would make the bishop move illegal.  For similar reasons, white could not have just moved the rook from e1 to f1.

That leaves only one possible move for white to have just made: kingside castling.

Since white just castled, black had to have promoted on d1 or f1.  If black had promoted to a queen or rook, there would have been a check where white would have either moved the king or captured the checking piece.  Since we have no room for an extra capture, this means that black could not have promoted to one of those pieces.

Which means that black promoted either to a knight or a bishop.  But we know that the promoted piece was captured on a5, b4, or c3 - all of which are dark squares.  The promotion happened on d1 or f1 - both of which are light squares.  If black promoted to a bishop, then it would have been on the wrong color square to have later been captured as required.

Thus, I have proven that black had to have promoted to a knight at some point in the game.

It isn't necessary to exactly recreate the game because there are many possible options, as you noted.  However, in every possible legal game that leads to that position, an underpromotion to a knight had to have occurred.

Here's the diagram of post #18 achieved without an N promotion:

And here's post #19 busted:

omnipaul, that is some fine, detailed analysis. Nice job!

As for the challenge of creating such a position where the side to move is not stipulated, I have an update. I'm sure it can be done with the castling theme, however, it became increasingly difficult so I ditched the idea and went for a completely different setup, using a retrocage, which is better.

Using a retrocage, I was able to do it. However I spotted potential for some even more bonus points, a position where both sides must have promoted to a knight. So I decided to go ahead and try to do it.

That turned out to be a lot harder then I expected 

However, after a very long time of experimenting, trying different ideas, spotting problems and fixing them, I believe I finally created a working position. Now, I'm not ruling out cooks completely here. I'm aware that the more complicated the position is, the bigger the potential for cooks is. I tried to check for a very long time though and could find none, and believe me, it was pretty tough trying to prevent all of them.

I'm also fairly certain that there are already compositions that meet these conditions, but for me it was pretty difficult to do... :)

Hmm, some trouble brewing...

Hah that's great, of course I knew that if there was a cook, it would be due to the weakness of the retrocage, something that I had to because of some limitations.

I won't give up on it just yet though, as I can still try different strategies / setups. For now, here's a position where only black had to promote a knight:

But why not...

You answer too quickly  I edited my board within 5 minutes, because a bishop promotion was possible.

But, one second. I'm trying to understand what you did here.

Alright, I think I understand. That's not possible now though as the promoted pawn must capture a piece to promote.

didnt the black pawn have to capture both white Knights to promote on d1/f1?

Yes, and that's a good thing as one of the conditions was that there will be no knights on the board. So black must have captured two knights, white must have captured three knights (one promoted, of course).

Ehh, ops. My edited position is no good because the b pawn does not need to promote to allow white to play cxb.

These are small annoying details, but they should be easy to fix with a few cosmetic changes.

Anyway I need to go now so I won't have time to fix it until tomorrow, see you later 

OK, my turn to get cooked.

As for the two knights promotions, I'm pretty sure this revised position does the trick.

What was wrong before: My retrocage was flawed. But now, I believe it is rock solid. This is important as the whole position relies on it. The move d2xe3 should lock the position and every piece must be where it is (except for the rook on h3 which can jump from h3 to h4 freely). What's different is basically a resource I haven't thought of before, I don't really need d2xe3 to free the bishop, or the bishop and rook. This allowd me to stick extra pieces in the retrocage to make it work.

d2xe3 allows a black pawn to promote on the d file with no captures. Only a knight or a bishop would not mate white, but a bishop won't do because white needs to capture on a7 - a dark square. So, white captures the promoted knight with his b pawn and promotes on a8, to a knight as well, as that is the only piece that can jump to h4 and be captured by black's pawn finally.

The position is really similar, so most of the analysis is the same. Black's h pawn couldn't have made no captures, it must have made at least 2 captures. The main difference is that white is only missing 3 pieces, while black is still missing 3 pieces. Black must have made 3 captures, which account for all of white's missing pieces. But for that, white must have promoted his b pawn by bxa7 (any other approach requires too many captures). The move bxa7 must be executed after the retrocage is locked with d2xe3.

Here's a continuation from the critical position, reaching the final position, which is the intended diagram:

Ouch - missed that white could simply play PfxPe.

Let's try:

Looks good - I don't see a cook.

Here is the predecessor, showing not only an N promotion, but also the Pronkin theme.

Andrej N. Frolkin
Andrej N. Kornilow
3441 Phenix 87 07-08/2000
version with colors reversed

Join the club... 

These things are quite common when composing, especially more sophisticated positions. It is simply hard to keep up with all the small details and possible things we've missed. This is why it's usually good to post these things here too, to proof test for cooks. I'll give the new position a look.

It took me a little while to understand the release of the position, since white's a1 rook is useless for capture, I imagined it off the board at first. But it is required for the tempo moves of course.

This time, fxe7 truely locks the retrocage, thus, everything falls into place. gxh3 must have been played at this point, but not a3, and cxb3 is impossible. Black can only advance his f pawn to promotion after fxe7 is executed. This means white must have his a1 rook otherwise he will run out of tempo moves.

The last sequence must be cxb3, capturing a promoted black piece, since after that we enter retrostalemate. Now, the promtoed black piece must have captured white's a1 rook. If we imagine a3 was played prior, any black piece other than a rook would do. But, after the capture of the rook, white will be one tempo short because he can't play cxb3. Therefore, a3 was not played prior to the rook capture. And the only way to capture the rook would then be with a promoted knight.

An elegant solution, well done. I will look at the study you posted when I have time.