Below you'll discover the solutions to the mate in four problems.
I'll give some comments to help you understand the way of thinking that leads to a solution. I hope this helps you to improve.
now if the King moves to c8 (this is the only possible place for the King, because he is in check on the other squares) there is 2. Ra8#. So 1.... Kc8 is mate in two.
The only other move to block the check is:
1... b6. After this move we have
This gives black the choice between interposing the Knight or moving the King away.
Interposing the Knight leads to:
3. Rxc7+, Ke8;
Moving the King leads to: 2.....Kc8 (or Ke8); 3. Nxd6#. Here you'll have to notice the knight delivering mate while protecting the rook at the same time.
Nr.2: 1.Rh6+, Kg4 (the only move);
2. Ne5+, Rxe5 (again, the only move);
3. Rf4+, Kxf4 (once again, the only possible move);
The difficulty in this puzzle is the unusual mating pattern.
Nr.3: 1.Qxh7+, Kxh7;
Now if 2....Kg8; 3.Rh8# is mate. Therefore the King has to move forward.
If you've made it this far, you may notice the e-file and the h-file being covered by the rooks.The King has very few squares (g6, f6 and f5). And we have the pieces to take away those squares. So we continue:
3. Bd3+ (only one square left), Kf6;
4.Bd4#. No pieces to interpose and no squares left.
Nr.4: If you noticed the open a-file, the bishop g2 pointing at b7, and the absence of a b7-defender, then you should have no problem finding the next sequence of moves.
1. Ra8+ (win a tempo in order to move the queen in attacking position), Kxa8;
2. Qa4+, Kb8;
3. Qa7+, Kc8;
Nr.5: Have you seen the holes at d6 and c7? And you may have noticed the queen covering c7 as well. This means the black King can't escape and has two squares left (e8 and d8). The only thing left is to find a sequence of moves (and a mating pattern) to take advantage.
1. Nd6+, Kd8 (only move);
2. Nxf7+ (getting rid of a defender), Ke8;
3. Nd6+ (important defender is gone, so now the mating attack starts), Kd8;
Nr.6: In this type of position you may be searching for a checkmate at g7. But did you notice the black king? It only has two squares available. So make it move around, while getting rid of an important defender.
1. Nh6+ (Knight to an attacking position), Kh8 (only move);
2. Nxf7+ (removing a defender) ,Kg8;
3. Nh6+ (making room to deliver mate), Kh8;
Nr.7: This type of position will probably be clear to you. The Queen has to reach the h-file to deliver mate on h7. There's only one defence to watch out for.
1. Bg6+, (attacking the black king, while at the same time closing the last line of defence for the black queen and rook. ) Kg8;
2. Rh8+ (sacrifices the rook to bring in the queen), Kxh8;
Nr.8: The king is a little exposed.
2.Rc8++, Ka7 (if 2....Kxc8, 3. Nb6 is mate);
Notice how h7 is undefended.
now taking the pawn is not an option due to 1...fxg6; 2.Qxg6 and 3. Qh6#.
1....Qh3+; 2. Rxh3,
the threat Qh7# has to be dealt with and fxg6 is still bad. The only other try is
2....Nxf6; covering the h7 square.
3. gxf7++, Kxf7; 4. Qg6#;