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Draw. 1.a7 or Bf3 draws cause black Rook is able to take both white Pawns.
At first glance starting with Kg6-Kg7 looks like a win, whilst the black Rook & King bother eachother stopping both pawns.I stick with a win for white.
A bit tricky! White has 2 passed pawns 2 squares away from queening; Black has 2 passed pawns 3 and 4 squares from queening. White just needs to queen and the queen will easily stop the black passed pawns and rook.The position is a win for white! 1.Kg6! Now Black Rook can no longer handle 2 passed pawns.>A-1...Rxg4.2.f7!.>>A1-2...Ra4.3.f8=Q+>>A2-2...Ke7.3.a7!.Ra4.4.Kg7!.Rxa7.5.f8=Q+.Ke6+.6.Kg6!>>A3-2...Rf4.3.a7!.Rxf7.4.a8=Q+.Ke7.5.Qa7+.Kd6.6.Qxf7>B-1...Ke8.2.Kg7!.Rf2.3.a7! and queens>C-1...Rf2.2.a7!>>C1-2....Rxf6+.3.Kxf6. and 4.a8=Q+>>C2-2....Ke8.3.a8=Q+>>C3-2...Kc7.3.Bf5! and f8 queens!>>C4-2... Ra2.3,f7!.>>>C41-3...Rxa7.4.f8=Q+>>>C42-3...Ke7.4.Kg7!.and 5.f8=Q+>>>C43-3...Ra6+.4.Be6!.Rxe6+.5.Kxg5 and queens at a8 or f8!>>C5-2....any pawn move.3.a8=Q+>D-1...Ra2.the toughest.2.Be2!>>D1-2...Rxe2.3.f7!>>>D11-3...Ra2.4.f8=Q+>>>D12-3...Ke7.4.a7!.Ra2.5.Kg7!.Rxa7.6.f8=Q+.Ke6+.7.Kg6!>>>D13-3...Rf2.3.a7!.Rxf7.4.a8=Q+.Ke7.5.Qa7+.Kd6.6.Qxf7>>D2-2...Kc7.3.f7! and 4.f8=Q>>D3-2...Ke8.3.Kg7! followed by 4.f7+ and 5.f8=Q>>D4-2....pawn move.3.f7!.Ke7.4.Kg7! and queens at f8.Having worked it out, it seems simple to advance f pawn when BR is not on f file and advance a pawn when BR is on f file! of course care is to be taken that BR is not allowed to capture a pawn with check or pin an otherwise queening pawn. Harry
1.Kg6 Rxg4(1... Ra2 2.Be2 Rxe2 3.f7 Ke7 4.a7 Ra2 5.Kg7 transposes.)(1... Ke8 2.Kg7 also wins)2.f7 Ke73.a7 Ra44.Kg7 Rxa75.f8=Q+ Ke6+ 6.Kg6 Kd5 7.Kxg5
1. Ke6! wins.
I remember this puzzle, and I seem to have gotten it hilariously wrong the last time, too. For some reason, I thought the following line was key:1. Kg6! Rg42. f7 Ke73. Kg7??Yikes! White wins with the pretty obvious 3.a7 here:3. a7! Ra4 (Rf7 4.a8Q)4. Kg7!And now white must queen a pawn. Probably best at this point is to just concede the queen at f8 and try to reconnect the king to the pawns by playing an immediate Ke6:4. ......Ke6 (Ra7 5.f8Q+-)5. f8Q! Ra76. Kg6And with the black king cut off at the moment from the pawns, it looks winning for white from here. Black cannot save the g-pawn by pushing it since Qf5+ wins the pawn, I can't even be sure he doesn't lose rook by playing g4. I think white wins this.
White wins. Kg6, Ra2, Be2!
Kg6 and white wins
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