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Bg3
1. Be3 Qxe6
2. Rxb8+ Kd7
3. Kxe6 Rxd8 white wins
IF
1. Be3 Na6
2. Rc6+ Kb7
3. Rb6+ Kc8(…Ka7 leads to mate Rxa7+)
4. Rc6+ Kb7
5. Rb6+ Kc8 draw with perpetual
1. Be3 Qxe6
2. Rxb8+ Kd7
3. Kxe6 Rxd8 white wins
IF
1. Be3 Na6
2. Rc6+ Kb7
3. Rb6+ Kc8(…Ka7 leads to mate Rxa7+)
4. Rc6+ Kb7
5. Rb6+ Kc8 draw with perpetual
BG3
BG3
1.Bg3 Qxe6
(1…Rxe6 2.Rxb8#)
(1…a3+ 2.Kxa3)
(1…Na6 2.Qg6 Rf8)
2.Rxb8+ Kd7 3.dxe6+ Kxe6 4.Rbxd8 Rxd8 5.Rxd8 Kf6 6.c4 g5 7.c5 f4 8.Bh2 Ke7 and White can by neutralizing the pawns
1.Bg3 Na6 2.Qg6 Rf8 3.Rxa6 Rf6 4.Ra8+ Kb7 5.Rxd8 Qxd8 6.Qxg7+ Ka8
Bg3 is the key, now only move is Qxe6 so that K can escape on d7. Then Rxb8+ kd7, pxe6+(double check so king has to move and only ke6 is less damaage. kxe6, RbxRd8 and thats heavy loss of meterials for black.
Rxb8+ Kxg8
Bg3+
atef from Malaysia
Bg3
1. Bg3! Qxe6 (Rxe6?? Rxb8#. Alternative below.)
2. Rxb8+ Kd7
3. dxe6++ Kxe6
4. R1xd8
is heavily up with material.
Or (seeminglyly critical):
1. … Na6 (f4 Bxf4)
2. Qxd7+ Rxd7/Kxd7
3. Rxa6
should be nicely up with a bishop.
This was almost to easy, what have I overlooked here?
Or:
1. Bg3! Nc6? (Rxe6?? looses immediately, Qxe6? looses quickly, knight sack Na6 was only alternative I found)
2. Rxc3+ Kb7
3. Rc7+ Qxc7
4. Bxc7 Kxc7
To the comments I can see here so far:
1. Bg3 Na6
is the line that has different suggestions for continuation in different answers here (not all found it at all).
I guess this is the best black has, but still easy to win with immediate exchange of queens before taking the knight:
2. Qxd7+ Rxd7/Kxd7
3. Rxa6
Black has no compensation for the sacked knight, and no pawn ideas.
h-pawn is still watched by Bg3 (Rh8 Rh1).
I still can’t see why this was called “difficult challenge”.
This is a win for white not draw by perpetual check as outlined above.
There are several features to take into account.
A.Black is effectively 4 pawns up with advanced pawns. So suggestions like winning a knight alone may be insufficient to win even if possible. (e.g. pht has overlooked taking 1. Bg3 Na6, 2. Q*d7+ R*d7, 3 R*a6 deos not win material; or in Ravi’s line, why play after 1. Bg3, Na6 2. Qg6 Rf8 3. R*a6 Rf6??)
B. There are several features to utilize for white: The gaining of a tempo to have the rook at b6 not c6; the passed pawn at d5. (This is a reason why the main line wins easily but not shown below).
C. Most important one must think deeper than the perpetual check Vignesh suggests. 1. Be3, Na6, 2. Rc6+ Kb7, 3. Rb6+ Kc8, 4. Rc6+ Kb7, 5. Rb6+ Kc8.
D. Finally there is an appropriate quiet Q move Qg6 at the correct time.
Here is a winning line:
1 Bg3 Na6
2 Rc6+! (this changes the tenor) Kb7 and now
3 Qg6! ( the quiet move but needed to get out the queen threat) Nb8 (the only move as otherwise Nc7, R*c7 wins material)
4. Rb6+ (so here is the required tempo == the check but with the B covering c7 and h8 the King must go to Ka7) Ka7. Now the exchange of B for N is possible.
5 Bxb8+! Rxb8
6 Ra6+ Kb7
7 Qb6+ Kc8
8 Qc5+ Kb7
(alternative is 8. … Kd8 9. Ra7 Qc8 10. Qd6+ Qd7 11. Q*d7 ++)
9 Rb6+ Ka8
10 Qa5+ Qa7
11 Ra6 and queen is pinned. Rb7 but there is more material first
12 Qxa4! Rd8 (for example)
13 Rxa7+ wins easily.
Psyche
This is a win for white not draw by perpetual check as outlined above.
There are several features to take into account.
A.Black is effectively 4 pawns up with advanced pawns. So suggestions like winning a knight alone may be insufficient to win even if possible. (e.g. pht has overlooked taking 1. Bg3 Na6, 2. Q*d7+ R*d7, 3 R*a6 deos not win material; or in Ravi’s line, why play after 1. Bg3, Na6 2. Qg6 Rf8 3. R*a6 Rf6??)
B. There are several features to utilize for white: The gaining of a tempo to have the rook at b6 not c6; the passed pawn at d5. (This is a reason why the main line wins easily but not shown below).
C. Most important one must think deeper than the perpetual check Vignesh suggests. 1. Be3, Na6, 2. Rc6+ Kb7, 3. Rb6+ Kc8, 4. Rc6+ Kb7, 5. Rb6+ Kc8.
D. Finally there is an appropriate quiet Q move Qg6 at the correct time.
Here is a winning line:
1 Bg3 Na6
2 Rc6+! (this changes the tenor) Kb7 and now
3 Qg6! ( the quiet move but needed to get out the queen threat) Nb8 (the only move as otherwise Nc7, R*c7 wins material)
4. Rb6+ (so here is the required tempo == the check but with the B covering c7 and h8 the King must go to Ka7) Ka7. Now the exchange of B for N is possible.
5 Bxb8+! Rxb8
6 Ra6+ Kb7
7 Qb6+ Kc8
8 Qc5+ Kb7
(alternative is 8. … Kd8 9. Ra7 Qc8 10. Qd6+ Qd7 11. Q*d7 ++)
9 Rb6+ Ka8
10 Qa5+ Qa7
11 Ra6 and queen is pinned. Rb7 but there is more material first
12 Qxa4! Rd8 (for example)
13 Rxa7+ wins easily.
Psyche