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1.... a2 2. Kd3 e2 3. Kxe2 Rh1 4. Rxa2 Rh2+ 5. Ke3 Rxa2 and black wins endgame K versus K+R
1.... a2 followed by a hail of checks (White can't take the a-pawn because of ...Rh2+) until the black K gets to the b-file, then the white R moves away and Black plays ...Rh1. A hail of checks might again follow, but eventually white has the lovely choice of giving his R for the a-pawn on a2 or a1.
I think a2 is the key move. The white rook can't capture because it will be in alignment with the white king and black will capture it after checking the king.The white king can not step to the back row because then the a pawn queens and the white rook will be forced to capture and again be lost to a skewer.Any other move by the white rook or white king allows the black king to walk to the b file and queens the a pawn or forces the capture of the white rook.
For clarity, after1. --- a22. Kd3(any white rook move off the a file loses the white rook or allows the a2 pawn to queen. any white rook move along the a file allows the black king to approach)then comes2. --- Ke6and after3. Rxa2(anything else allows the black king to approach or one of the pawns to queen)there is3. --- e2+4. Kxe2 Rh2+5. King any Rxa2and the only piece left is the black rook.
Pretty simple, I think:1. .....a2!White can't take the pawn at a2 because of the skewer from h2 by the black rook, and black is threatening Rh1 supporting the pawn's advance. White can check the black king, or he can move the king to d3. Let's study the latter of these ideas first:2. Kd3 e2!3. Ke2Or [3.Kd2 e1Q 4.Ke1 Rh1-+]. Continuing:3. .....Rh1 and white loses his rook at either a2 or a1- his choice.Now let's make sure there are no ways to endlessly harass the white king:1. .....a22. Ra6 Ke53. Ra5 Kd44. Ra4 Kc35. Ra8Clearly, 5.Ra3 loses to Kb2 followed by a1Q, but 5.Ra8 isn't going to be any better:5. .....Rh1 (preparing a1Q)6. Rc8 Kd4 and clearly black can walk the rook down this way, too.
easy win...1 .. a2!
a2 for black is the only good move for the win.
No draw. Its an easy win for black1. a2 black can not take on a2 because of Rh2+ pinning rook.1.--- Kd3 now black can take on a22. e2 Kxe2 (forced)3. Rh1 black threatening a1Q3.--- Rxa2 (forced)4. Rh2+ now white rook is pinned and easy win for black
1...a2 2.Ra6+(2.Rxa2 Rh2+ 3.Kxe3 Rxa2)(2.Ra3 Rh1 3.Ra6+ Ke5 4.Ra5+ Kd4 5.Ra4+ Kc3 6.Ra3+ Kb4 7.Rxa2 Rh2+ 8.Kxe3 Rxa2 9.Kd4)2...Ke5 3.Ra5+ Kd4 4.Ra4+ Kc3 5.Ra8 Rh2+ 6.Kxe3 Rb2 7.Rc8+ Kb3 8.Rb8+ Kc2 9.Ra8 Kb1 10.Kd3 a1=Q 11.Rxa1+ Kxa1
1. ... a2!If,2. Rxa2 Rh2+ wins the rook and the game.If,2. Ra6+/Kd3 Black should be able to promote one of the pawns easily
1.-a2 2.Kd3 (2.Rxa2? Rh2+) 2.-e2+ 3.Kxe2 Rh1! 0-1May Gyula Sax rest in peace.
1. ... a2! What can White do? Clearly, the rook cannot take the pawn, see2. Rxa2 Rh2+3. e.g. Kxe3 Rxa2 and wins.So, the white rook has to stay on the a-file. The basic threat after 1. ... a2 is 2. ... Rh1, forcing the rook to take on a2. This is, as we have seen, deadly, as long as the white king is placed on the second rank. On the other hand, the king cannot go to the first rank, because of Rh1+ followed by a1=Q. Rook-checks from the a-file do not change anything. So:2. Kd3 trying to enable the rook to take on a2. But:2. .... e2!3. Kxe2 what else? Now the king is again on the second rank, so:3. ... Rh14. Rxa2 Rh2+5. K anywhere Rxa2 and wins.
Easy draw? Yeah right. If you want to, white wins! But...black wins, by force. Either he promotes the a-pawn or white gives his Rook.Figure it out yourself. Hint: start with a2.
1...a22.kd3... Black king moves towards b file and down towards a2 pawn.
1... a2!it's obvious with 2.Txa2 and 2.Ke1, black looses easily. 2 Kd3, Ke63 Ke2, Kd64 Kd3, Kc65 Ke2, Kb6and black wins ...
a2, then move the king to the queen side to atack the white rook
1...a2, then move the king to the queen side to atack the white rook. If rook take the pawn, then Rh2 check.
This looks kind of elementary:1. ... a2If white takes on a2, he looses rook to Rh2+, so he won't.But what else then?If Kd1/Ke1/Kf1 then a1=Q+! Rxa1 Rh1+ looses rook in the same way.To delay things with checks doesn't help either, black king will simply approach a-file.White must try:2. Kd3 e2!3. Kxe2 (what else?) Rh1!!Either a1=Q or Rh2+ must now come next, in either case it's0 - 1
The main line: 1). ... a2 2). Kd3 e2+3). Kxe2 Rh14). Rxa2 Rh2+and the rook on a2 is for free.
1.....a2!White rook cannot leave a-file as black a2 will queen. If White keeps checking black king, black king moves to b file when checks stop. A. If White plays 2.Rxa2 (straightaway or later when when checks stop) ...Rh2+ wins the rook and the game. Hence white cannot take a2 pawnB. If white simply plays rook along a-file away from black king and does not take a2 pawn eg., 2. Ra8 (straightaway or later when checks stop)then 2....Rh1!! (threatening 3...a1=Q) wins3.Rxa2.Rh2+ 4. Kxe3.Rxa2 etcC. If 2.K-first rank..a1=Q+!3. Rxa1..Rh1+ 4. K-second rank..Rxa1 winningD. If 2.Kd3..e2!!3. Kxe2 Rh1! threatening a1=Q4. Rxa2.Rh2+5. K any Rxa2 winning!Harry3
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