|Position 1: Black to move and draw|
Solving this requires a keen eye for tactics. Take a look at the highlighted squares::
You can see that White's knights and king take away the c4, e4, d2 e2, and e3 squares from the Black king. If White's Queen is lured onto b2, it would deny Black's king the remaining squares around him, thus creating stalemate. Black does this by throwing in a decoy: 1... Re2+ 2. Kd1 Rb2! (with the dual threat of Rxb8 and Rb1#) 3.. Qxb2 stalemate.
With this in mind, we move on to the 2nd position:
Troitzky Endgame Study
|Position 2: White to move and win|
1... Bxf8 2. b7!
Not} 2. Nf5+? Kd3 3. b7 Bb4+ 4. Kd1 (4. Kf2 Bc5+ 5. Kf3 Ba7) 4... Rxa2 5. Kc1 Ba3+ with mate to follow.
We reach a position similar to the main line after 2... Bb4+ 3. Kd1 Bd6 4. Nf5+
Removing the defender of the b8 square.
Setting up a stalemate trap. On the other hand Black is toast after 3... Kd5 4. Nxd6 Kxd6 5. b8=Q+
4. Nxd6 Rxa2
White wins in this position, but it leaves many heads scratching: Why not promote to a queen? Let's take a look at what happens after 5. b8=Q?? (D)
And we reach the same position as our first puzzle! From there we already know that Black forces a draw with Re2+ 6. Kd1 Rb2! 7. Qxb2 stalemate.
|Position 3: Black to move and win|
If it were White to move, he would be in zugzwang: 1. Kc2 Kc4 and White's king must give up the b3 square. Thus, Black needs to lose a tempo to get the same position with White to move.
Exploiting White's lack of space to employ a triangulation technique. The immediate 1... Kc4? makes no progress after 2. Kc2
2. Kb1 Kd5!
Once again Black achieves nothing after 2... Kc4? 3. Kc2
Or 3. Kc2 Kc4 4. Kc1 Kb3 winning.
We have reached the original position but with White to move. Now White is in zugzwang.
4. Kb1 Kd3 -+
5. Kc1 Kb3
The a3 pawn falls and Black will promote his pawns.
All the best for your exams!