Deductive Puzzle #43

As you can see, White seems to have Bishops on both h2 and h4, but only one of them is real. Depending which one it illusionary, White is in an excellent position. Which of the two bishops on h2 and h4 must be unreal for White to have a certain win in two moves?

i am so confused as to how the bishops could contribute to a mate in 2... hmmm, one of the bishops must take some part in the mate in 2 (not neccesarily moving it).

This one confounds me a little.  I wondered if one of the Bishops wasn't in the way.  Note that it doesn't say mate in 2, but a certain win in two moves which could just mean an insurmountable advantage.  As with the other puzzles of this nature I suspect you have to construct some of the position's history but I just can't see what's relevant yet.

oh right, thanks TheGrobe.

Maybe something to do with Ne3?... Assuming that the bishop is on h2 to limit more squares for the queen to run to... but it doesn't seem to wor MAJORLY, and make a certain win.

I bet it has something to do with Black's castling rights. However, I don't know what to make of the phrase "a certain win in two moves". If it means mate in two, then that's an unnecessarily complicated way of putting it, and if White can get an advantage in two moves surely he already has one. You could make some argument about material deficit, etc. but then you're getting into something completely aside from the chess position.

I was just taking it word for word from the book. But yes, it is mate in two.

Time to start counting captures.

Two captures by black:  White's light-sqaured Bishop on g6 and then White's h-pawn on f6 (possibly after promotion).

At least one capture by White on c3 -- necessarily Black's rook as the square is not the same colour as Black's missing bishop and there are not enough missing White peices for Black's missing e-pawn to have captured his way over there.  Knowing that the Queen-side rook escaped means that Black's king has moved as the pawn structure doesn't allow its escape by any other means which means that Black cannot castle.

Just a Black's e-pawn can't have captured it's way to the c-file, it also can't have found its way to the f-file to be captured by White's h-pawn so the capture of White's h-pawn had to have occurred after promotion (or the peice it replaced was captured, but both amount to the same thing).

Now what does any of this have to do with the extra Bishop...?

I think the h4 bishop is real. I think it might have somthing to do with taking the bishop on g5 and allowing white's knight to go to h6 if black castles first. Mabye Qa6, threatning mate on c8.

Qa6, would force black to castle.

Black can't castle.  See above.

That seems to be the move -- Qa6 followed by Qc8#, and since we know Black can't castle there's no defense.

The bishops are completely irrelevant to this deduction though.

You are missing something Grobe...

Hmmm, when I look again I realize that Black's e-pawn could have promoted and been the piece captured on c3, so it wasn't necessarily the Rook that was captured there and the King need not have moved to allow it out therefor the conclusion that Black can no longer castle is incorrect.

I think that proving Black can no longer castle, however, is the key to this puzzle.  Now what do the Bishops have to do with Black's castling rights?

A-ha!

So in order for White's dark-sqaured Bishop to escape the capture on c6 must have occurred meaning the promotion of Black's e-pawn must have occurred.

In order for this to have happened, however, it must have somehow gotten around White's e-pawn.  Since we've accounted for White's missing pieces Black's e-pawn can't have made two captures and therefor it must have been White's e-pawn that captured to get out  of the way, and then again to get back on the e-file accounting for Black's missing Bishop and Rook and again necessitating a King move for the Rook to escape.

Again, though it doesn't matter which of the two Bishops is real...

Hmm....

Why couldn't black's e pawn have captured on  f2?

I see what's still wrong with my analysis, there's no way Black's light squared Bishop could have escaped....

 Why not?

Jeeze... I'm all turned around now.  That's not right either.

The promoted pawn was not necessarily the e-pawn -- it could have been the h-pawn that promoted, and the g-pawn was pushed to g6 as opposed to being the h-pawn and having captured there.  This frees up a missing White peice, the light sqaured Bishop, to be captured elsewhere.  Since there's only one missing peice, the h-pawn must have promoted on g1, and in order to do so it must have captured on g2 while the h-pawn was still on h2.  This means that the g3 pawn push happened while the h-pawn was still on h2 and the h2 Bishop can't have arrived there.

In this scenario, however, we still need to prove that Black can't castle -- I think it may lie in proving that the h-pawn promoted on h8 and that the rook must have moved.

No reason -- disregard that nonsense it's incorrect for all sorts of reasons.