Solution for October combinations

If you select the option on the menu just under the header on this blog Monthly combinations, you can see only the articles with the exercises and solutions for the exercises.
Solving the combinations are one of the most important parts of chess training.
On this blog, during the time, I collected about 130 combinations which have high instructional value.
They are free to use for all the readers, and the experienced eye can spot the most important parts of the combinations, for their own training, or for the training of the others.
Here are the solutions for the month of October.

In this position Black just took the rook on b1. White has wide choice of captures, but one of these leads straight to the mate.

1. Bxf7+, Kh8
2. Qf8+!!

After this check, everything is over.
Maybe 2. Bxe8 wins as well, as there is a mate threat on f8, but queen sacrifice is completely forcing.

White king is so weakly placed that Black only needs to restore the coordination between his pieces, even if it cost material.

1...Rh1!
2. Rxe8+, Kg7

White has not useful checks, and there are no ways that he can protect his king.
Black wins.

This example is somehow similar the the previous one.
The main role is again the coordination between the queen and the rook.

1...Qh8!

Only this move, not 1...Qh6 2. Rh4!.

2. Kf3, Qh5+

and Black will win.

This combination is harder then the previous three.

1... Rg2+!!
2. Kxg2, Qg5+
3. Kf1 

In the game 3.Kxf3, Qg3+ 4. Ke2, Qg2+ 5. Ke1 (forced)
5...Qxc2 -+

3...Bh3+!!
4. Rxh3, Qg1+ -+

This combination has a lot of elements included.

1. Rxf7!, Rxf7
2. Bxf7+, Kxf7

The first part of the combination is to force the black king on f7.

3. Nd5!

Now it is not possible to take the knight as after e5-e6+ White would win the queen on c7.
Black now can retreat his queen on many squares, and White is winning in any case.
I will show just the most logical and beautiful line.

3...Qa7
4. Rf1+, Kg8
5. Ne7+!

This is possible just because the queen is hanging on a7 and Black can not capture this knight with his bishop.

5...Kh8
6. Rf7, g6
7. Rxh7+!, Kxh7
8. Qxg6+, Kh8
9. Qh6 #