1. cxb8 = N is mate.
Maybe instead is is better to replace the a8 rook with a queen. The pawn on a6 gives it away that the king attacks the b7 knight somehow, and therefore the king is on c8.
Tricky Checkmate


1. cxb8 = N is mate.
Maybe instead is is better to replace the a8 rook with a queen. The pawn on a6 gives it away that the king attacks the b7 knight somehow, and therefore the king is on c8.
Nice observation. But the Black King might be on another square.

cxb8=N can mate black in all situations
Let's see. Is white in check?
If white is not in check -> Black king at c8 -> cxb8=N is mate.
If white is in check -> How did black check white?
Let us consider all possibilities:
1. Normal move of Rook -> impossible, since every square is a check to the white king
2. Pawn promotion -> impossible, this is the 8th rank
3. Discovery check -> This is the only possible situation. The black king moved away from c8 (only possibility) to d7. Now the king is at d7, cxb8=N is mate.

cxb8=N can mate black in all situations
Let's see. Is white in check?
If white is not in check -> Black king at c8 -> cxb8=N is mate.
If white is in check -> How did black check white?
Let us consider all possibilities:
1. Normal move of Rook -> impossible, since every square is a check to the white king
2. Pawn promotion -> impossible, this is the 8th rank
3. Discovery check -> This is the only possible situation. The black king moved away from c8 (only possibility) to d7. Now the king is at d7, cxb8=N is mate.
Good job, this is indeed the complete solution.
The Black King has made himself invisible! But he won't remain invincible...
White to Mate in 1