# Can White Castle? #2

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?

• Both were very interesting although not that hard. Keep it up! Jun 21, 2019 at 13:23
• @ArnaudMortier it turned out to be a little bit harder - see the updated answer. Jun 21, 2019 at 19:12
• @Glorfindel I hadn't looked at your answer when I wrote that. Jun 21, 2019 at 20:51
• @shoopi when writing long answers I always end up slower than others and have to dump my work :/ Jun 22, 2019 at 0:13
• 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!
– Bass
Jun 24, 2019 at 11:31

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.

• 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). Jun 21, 2019 at 18:45
• @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 ... Jun 21, 2019 at 18:56
• That's right :) Jun 21, 2019 at 18:59