A Truly Amazing Miniature

This puzzle blew my mind the first time I saw it about a month ago. White has two logical moves to attempt a draw. Your task is to show why one of them draws for white while the second one loses. Difficulty level- extreme.

5k2/8/5r2/1RRK4/6p1/8/5p2/8 w - - 0 1

I have no idea how to solve this puzzle for now.

White to play draws, but with precise play only.

  1. Rc1? Rf5+ 2. Kc4 Rxb5 3. Kxb5 g3 wins for Black. 2. Ke4 Rxb5 3. Kf4 also doesn't work due to 3... Rf5+! 4. Kxf5 g3. Now, 5. Kf6 Ke8 6. Ke6 Kd8 7. Rd1+ Kc1 and the BK escapes checks.

White can get is a draw with 1. Rb1! Rf5+ 2. Ke4! Rxc5 3. Kf4 Rf5+ (3... Rc4+ 4. Kg3 draws.) 4. Kxf5 g3, and now the fact that the R is on the b-file changes things. 5. Kf6! Ke8 (5... Kg8 6. Kg6) 6. Ke6! Kd8 7. Kd6 Kc8 8. Rc1+ Kb7 9. Rb1+ Ka6 10. Kc6! draws due to the mate threat in the other direction. An attempt to escape by going down loses: 10... Ka5 11. Kc5 Ka4 12. Kc4 Ka3 13. Kc3 Ka2? (13... Ka4 draws.), and now 14. Rf1! and now both 14... Ka3 Ra1# and 14... g2 15. Rxf2+ followed by 16. Rxg2 win for White.

We need to consider another line also after 1. Rb1. 1... g3 2. Rc3 g2 3. Rb7 Rf7 4. Rb8+ Kg7 5. Rg3 Kf6 6. Rf3+ Kg6 7. Rg3+ draws. 7... Kf5 8. Rg3+ Kg4 9. Rxf7 wins for White.

Umeshpn, the king doesn't truly escape in either variation, but when white has been forced to play 7.Rd1+ vs 8.Rc1+ this costs white exactly one tempo, which black uses to play g2, and that move means that when black has been forced to, for example, a6 followed by white's Kc6, black can now play f1(Q) or g1(Q) guarding the a1 square and the threatened mate. Other than that one nitpick of mine, well done!

The ultimate difference between 1.Rb1 and 1.Rc1 is these two positions: 8/8/k1K5/8/8/6p1/5p2/1R6 b - - 0 1 and 8/8/k1K5/8/8/8/5pp1/1R6 b - - 0 1.

Right. Or between these two: 8/8/k1K5/8/8/6p1/5p2/1R6 b - - 0 1 and 8/8/k1K5/8/8/6p1/5p2/1R6 w - - 0 1. Same position, Black's move and White's move.

Thanks for the correction. I stopped analyzing after 7. Rd1+ Kc7.

Yes, those two position, too. Where I really got hung up on this problem was in trying to avoid letting the black king off of the 8th rank- in other words, I thought both starting moves were losing, and spent an inordinate amount of time trying other beginning moves for white before giving up and going back to the choice of 1.Rc1 and 1.Rb1.

Yes. 1. Rb7, 1. Rc7, and the two checks are also candidate moves. I spent some time analyzing the checks, because I thought both 1. Rb1 and 1. Rc1 would lose to 1... Rf5+ and exchanging a pair of rooks. A lone rook has no chance against the advanced connected pawns. Once I discovered 2. Ke4! (in either variation), I had a feeling that one of 1. Rb1 and 1. Rc1 is the solution. Initially, I didn't see ...Rf5+, so thought 1... g3 is forced to avoid draw. Things got really complicated after I discovered ...Rf5+.

By ... Rf5+ above, I mean 3... Rf5+, not 1... Rf5+.

Alena, neither have I. LOL

I found the start really quickly- 1.Rb1/Rc1 Rf5 2.Ke4 Rxc5/b5 3.Kf4 Rf5 4.Kxf5 g3 5.Kf6- literally in the first couple of minutes, but then saw the black king getting off the 8th rank in both lines- I completely missed that white gets him back on the edge without allowing g2 in the interim- probably because I had analyzed 1.Rc1 first and saw that g2 wins for black- I couldn't see the tempo difference and abandoned both ideas. After that, I spent almost a day trying to make the two moves 1.Rc7 and 1.Rb7 work as a defense- sure I was just missing something in all the winning lines for black. After I had closed out all the possibilites for the alternative ideas, I was forced to go back to the beginning.