Following on my previous puzzle that was well received (here).
Note that this one is a lot shorter / easier, so feel free to participate!
Can White Castle?
$\begingroup$
$\endgroup$
7
-
$\begingroup$ Both were very interesting although not that hard. Keep it up! $\endgroup$– Arnaud MortierCommented Jun 21, 2019 at 13:23
-
1$\begingroup$ @ArnaudMortier it turned out to be a little bit harder - see the updated answer. $\endgroup$– GlorfindelCommented Jun 21, 2019 at 19:12
-
$\begingroup$ @Glorfindel I hadn't looked at your answer when I wrote that. $\endgroup$– Arnaud MortierCommented Jun 21, 2019 at 20:51
-
1$\begingroup$ @shoopi when writing long answers I always end up slower than others and have to dump my work :/ $\endgroup$– Arnaud MortierCommented Jun 22, 2019 at 0:13
-
3$\begingroup$ While this puzzle may have used more words than the earlier one, the story it tells is no less captivating! The difference in vote counts reflects (I believe) mostly the fact that this puzzle was posted on weekend, and therefore stood no chance of getting the "Hot Network Questions" boost that's pretty much the only way to get past 50 upvotes on this site. Brilliant work again, OP, and please keep posting if you have any more of these! $\endgroup$– BassCommented Jun 24, 2019 at 11:31
|
Show 2 more comments
2 Answers
$\begingroup$
$\endgroup$
3
The answer is
yes, White can castle.
Reasoning:
The white knight on c8 can't have arrived from a7 or e7, since the pawns there are still in the same place. d6 doesn't work either, as from there it would give check. There is some wiggle room for the king if the queen is on c8, but the knight needs to be on c8 already when the king moves to e8, and then the queen can't reach d8 anymore.
So
The white knight arrived there from b6 before Black played b7-b6, so it captured the light-colored bishop and the one on b7 is a promoted h-pawn.
This could only happen
when it promoted on f1 or h1; since White has 8 pawns, it needs to have captured twice to get to f1 or h1. But one of those captures must have been White's dark-colored bishop, so h7-h5-h4-h3xg2xf1=B is not possible.
It can't reach g2 in another way, so something like h7-h5xg4-g3xf2-f1=B must have happened, but that is only possible if the white king was temporarily somewhere else on the board; it must have moved and White cannot castle anymore.After a hint by the OP, I found a way to reach g2 while capturing on a dark square:
White's f and g pawns
must have captured as well; the pawn on f4 is the g-pawn and it captured Black's king's rook or knight to make way for the black pawn; after it reached g2, the white f-pawn captured the other piece on g3.
So
one possible way to get to the current position with White able to castle
would be
1. b3 h5 2. Ba3 h4 3. Bd6 Rh6 4. Bg3 hxg3 5. Nf3 Rf6 6. Ne5 Rf3 7. gxf3 Nh6 8. Nc4 g2 9. Nb6 Nf5 10. Nxc8 gxf1=B 11. f4 Ng3 12. fxg3 Bg2 13. Qc1 b6 14. Qd1 Bb7
The game can be replayed here.
answered Jun 21, 2019 at 11:57
-
$\begingroup$ Good analysis. You are correct that rot13(Oynpx zhfg unir cebzbgrq gur yvtug-fdhner ovfubc, ohg gurer vf nabgure jnl sbe gur cnja gb ernpu t2). $\endgroup$– shoopiCommented Jun 21, 2019 at 18:45
-
$\begingroup$ @shoopi Lbh'er evtug - vs Juvgr znantrf gb cynl t2ks3-s4 naq (nsgre Oynpx cynlf u7-u5-u4kt3-t2) s2kt3, vg fubhyq jbex. Gubfr juvgr cnjaf pna pncgher n oynpx ebbx, xavtug naq ovfubc. Yrg zr hcqngr zl nafjre ... $\endgroup$ Commented Jun 21, 2019 at 18:56
-
$\begingroup$
$\endgroup$
This is the same as Glorfindel's answer, but written in a way that helps the reader discover the solution themselves. Similar to the answer on shoopi's first puzzle.
How did White's knight arrive on c8?
Could it have arrived from the 7th rank?
It can't have arrived from a7 or e7, as Black's pawns there have not moved.
Could it have arrived from d6?
White's knight would have checked the king from here. A possibility to consider is that Black played b6 -> Bb7 -> Be4 (out of the way) -> Qb8 -> Kd8 to allow passage for the knight. However, due to the pawn placement, this possibility leaves no space for Black's queen to return to the starting square. Therefore, this is impossible.
Therefore:
The only possibility is that the knight arrived from b6.
How did Black's bishop arrive on b7?
The problem with there being a bishop on b7 is that we've just deduced that White's knight travelled through b6. Black seemingly must play b6 before the bishop can be developed to b7. Contradiction?
The only possibility is:
The bishop on b7 in the final position is in fact Black's promoted h-pawn.
Where was Black's promotion square?
The pawn must have promoted on a light square. The only option is f1.
How did Black reach this promotion square?
Black must make two captures with the h-pawn in order to reach f1. Counting White's material, they have only lost the bishop pair. As such, both bishops must be captured by the h-pawn.
Where did the h-pawn's captures occur?
Looking at White's kingside pawn structure, it appears that there must have been a capture either from g4 to f3, or from h3 to g2.
Did a capture occur from g4?
This is impossible, as pushing the pawn to f2 is unavoidable and checks White's king.
Did a capture occur from h3?
This is also impossible, as this implies two light square captures. This contradicts with White's material loss of a bishop pair.
So how did Black pull off this impossible promotion?
The final key to the puzzle lies in Black's lost material - a knight and a rook. White's f and g pawns have actually swapped files!
So the final order of operations (excluding padding that moves pieces where they need to go):
Black plays hxg5, capturing White's dark square bishop.
White plays gxf3, capturing one of Black's pieces.
Black, having pushed their pawn down the g file, plays gxf1 and promotes to a light square bishop.
White plays fxg3, capturing the other Black piece.
White plays Nb6xc8, capturing Black's light square bishop.
Black plays b6, and retreats their newly promoted bishop to b7.
