Deductive Puzzle #45

Which of the Black Knights is the promoted piece? No white Piece now on the board was promoted and the pawn on b3 came from b2.

Version 2: All White pieces on the board are original, and the White king has never moved. Now which Knight is the promoted one?

In version 1, Black's pawn would have had to have captured over to at least the b-file to promote and since White is only missing two pieces it would have had to have promoted on b1.  In order for it to get by the b pawn it would have had to have captured on bb2 meaning that the b2-b3 pawn push already happened before the promotion and there's no way it's the Knight on a1 since the only way it could have got there was via b3, before the promotion, or by promoting on a1 which can't have happened since there aren't enough missing pieces. 

But how did the White a pawn get into the right place to be captured on either b2 or the c-file?  It must have promoted (note that the hint says no piece on the board was promoted) and then got into position since there aren't enough Black pieces missing (one) to support any other possibility.

So how did it promote?  The only possibility is by capturing Black's missing queen on b7 and promoting on b8 which means that the Black b8-b7 pawn push happened before White's promotion, and as a result before Black's promotion and therefor there's no way that the Knight now on a8 is the promoted Knight as it couldn't have gotten to that square after that pawn push.

As a result, the only possibility is that the h8 Knight is the promoted one.

I'll leave part two for someone else.

I've got part two as well.  I liked these ones.

No-one?

I'll post the solution to part two in a few hours if no-one else does before then.

Well the knight on a1... the e pawn somehow got to capture the bishop on b7 then got to a1...? because a1 is the only promotion spot. And for that to happen, b3 must have been played so i PREDICT that is the promoted knight, although it seems im missing something because i don't know how the pawn from d7 got there...

Also, it must be a1 i guess because otherwise its the other two knights, and they seem to be in the same position, so if its not the a1 knight, then we dunno which knight it is at all from the 2 knights on the back rank. i definetly AM missing something... did the pawn somehow promote somewhere else apart from a1?

Ok, I can't help myself.  Here's the solution to #2:

We know that Black's d-pawn promoted.  In order to have done so it could have gotten past White's pawn chain in one of two ways:  Either by capturing over to the g-file (including a capture on b2 after the b2-b3 pawn push) or by capturing over to the half-open e-file.  If it captured over to the e-file we know it must have captured on d1 or f1 since White's king hasn't moved.

In either case, two captures of White pieces are required for Black to have promoted, which works because White is missing two pieces.  As with the last puzzle, the promotion can't have occurred on a1 because that would be one too many captures, so if it promoted via the b-file it promoted on b1.  This alone doesn't tell us that it's not the a1 Knight, but if we observe that both d1 and f1 are light coloured squares we can surmise that in the case where the promotion took place via the e-file White's missing dark-squared Bishop must have been captured first followed by the White promoted pawn on d1 or f1.  This means that in either case the b2-b3 pawn push must have occurred before Black promoted (to free the Bishop in the e-file case), and therefor the Knight on a1 must have also been there before Black promoted so it is not the promoted pawn.

We can also observe that Black is only missing one piece this time -- it's dark squared Bishop.  We know that White's pawn must have promoted in order for it to have subsequently have been captured on d1 or f1, however what about the case where Black promoted on b1?  In order for Black's pawn to have gotten over to the c-file to capture on b2 it must have captured something on the c-file.  It is White's pawn, that is missing however, and for it to have been captured on the c-file (or alternatively, b2 if the Bishop were captured on the c-file) it must have been promoted first because it would take too many captures to get it there as a pawn.  So we know that White's pawn promoted.

How did White's pawn promote?  With only one missing Black piece, there is only one option:  It captured over to the d-file by capturing Black's missing dark squared Bishop and promoted on d8.  This means that Black's dark-sqaured Bishop must have escaped, via it's only possible escape route, before it was captured, before White's pawn promoted, and before Black's pawn promoted.  Since this means that the g7-g6 pawn push must have happened before Black's pawn promoted, there's no way the promoted Knight could have gotten to h8 and it is therefor the a8 Knight that is the promoted pawn.

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