The mystery is that someone has just placed one extra black pawn on the board – there are 9 in total. Also, no matter which one is the added pawn, there always exists a mate in one move.
If the extra pawn was a7 – Qb6
If the extra pawn was b7 – Kc6
If the extra pawn was c4 – Qb4
If the extra pawn was d3 – Qe4
If the extra pawn was e3 – Bxf2
If the extra pawn was f7 – Ke6
If the extra pawn was g6 – Rg4
If the extra pawn was h3 – Rh4

The move is Rc6+. Then Black can play Rxh7.

The answer is Qa3#.

The white king is on c3. Since he cannot be currently on b3 (he will be in double check from the black rook and the black bishop), Black must be currently in check from the white bishop. That’s possible only if White has given a discovered check with his king. That’s possible only if on the previous move, the white king was on b3 and was in double check. The only possible way for this to happen is if Black gave two discovered checks at the same time. The one way to do this is if a black pawn on b4 captured a white pawn on c3 using en passant. Thus after b4xc3, the white king has just captured the black pawn on c3, and that is where he is currently hiding.

One possible solution is:
1.d3 h6 2.Bxh6 f5 3.Qd2 f4 4.Qxf4 a5 5.Qxc7 Kf7 6.g3 Kg6 7.Bg2 Kh5 8.Bxb7 Kg4 9.Nf3 Kh3 10.Bxc8 e5 11.Bxg7 e4 12.Kd2 e3+ 13.Kxe3 Kg2 14.Ng1 Kf1 15.Kf3 Ke1 16.Qxa5+ Bb4 17.Nc3+ Kd2 18.Rf1 Rh3 19.Bxd7 Nh6 20.Nd1 Kc1 21.Bxh6+ Kb1 22.Bc1 Na6 23.Kg2 Rc8 24.Bxh3 Rc3 25.Nxc3+ Ka1 26.Nb1 Nc5 27.Rd1 Be1 28.Qxe1 Ne4 29.Kf1 Nd2+ 30.Rxd2 Qd5 31.Qd1 Qg2+ 32.Ke1 Qf1+ 33.Bxf1

White plays Rh6. If Black moves the bishop, Rxh7 is a mate. If Black takes the rook, g7 is a mate.

The last move was white king takes black knight on c1.

8 moves example:
1. f3 Nf6
2. Kf2 Ng8
3. Ke3 Nf6
4. Kd3 Ng8
5. Ke4 Nf6
6. Ke3 NNg8
7. Kf2 Nf6
8. Ke1 Ng8
In order to see that 8 is the minimum number of moves, notice that Black could only move rooks and knights, and therefore he has made an even number of moves. This implies that White has made an odd number of moves, excluding the pawn on f3. This is possible only if he has placed his king on a white cell at some point and then returned it back to e1, which would take at least 8 moves.

e3 Rxe3
c3 Rxc3
Ka2 Ra3+
Kb1 Ra1+
Kc2 Rc1+
Kd3 Rc3+
Ke2 Re3+
Kf1 Re1+
Kg2 Rg1+
Kf3 Rxg3+
Ke2 Re3+
Kd1 Re1+
Kc2 Rc1+
Kb3 Rc3+
Ka2 Rxc7
Rh8+ Rc8
Rxc8#

Coming soon.