Excellent problem! Capturing a pawn is not a flaw, and a key move with 2 threats neither. It's more likely a plus since so many black defenses are capable of disarming both threats simultaneously! So where is the blemish? I don't know and therefore I see nothing wrong in bestowing a prize on this problem! Btw, Loshinsky is well-known as a top composer.
Mate in two (457)
"The unique 457†,with a key that brings the WR into play and creates a double threat,brilliantly shows 6 interferences on one orthogonal line." That is all he had to say about the puzzle,yet he marks it ... Is having two ways to mate against some defenses considered a blemish?.......He has 14 record puzzles in this book alone.
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Edit:
Ah, I misread your comment which was about "having 2 mates after a defense". I assume your "defense" disables both threats otherwise it is not a defense in the context of this theme which is "mate change after blocking a double threat". It would be a blemish if one of the new mates arising after a defense is dualed. But I don't see one! Do you?
No I just see double mates on weak defenses like pc1 ,but he has all those included in the moves section...I was just drawing at straws for an explanation of why he might think it a blemish....I only see one move that blocks both of the threats (Re7,Be6) a third threat Pxe8N is already there right?..The conventions can be a little confusing I think.
There is no 3rd threat because Qa5 covers d8. There are 8 moves blocking both checkmate threats, all refuted by different new mates! Try to find them because they are most instructive!
The fact that I consider a move like 1. ... Qa2 not a blemish, does not imply that the author does not. There are circumstances where it could be seen as a flaw. However, here it is not in my opinion because "blocking the double threat" is the theme! It is almost ridiculous to assume that alongside this theme there wouldn't be any weak defenses and dual checkmates as well.
But it is also possible that the dagger refers to a different flaw I didn't notice!
Ah, see another flaw. There are actually 9 different moves blocking both checkmates. The 3 Queen defenses are all met by the same checkmate cxd8=N#. That counts as a flaw though not a fatal one!
White in two by L. I. Loshinsky & G. S. Baev 1st prize 1933 †