r1qr1b2/1R3pkp/P2p2pN/p1nPp1Q1/bn2P3/4P1NP/PBBPp1P1/5RK1 w - - 0 1
Here is the proper FEN r1qr1b2/1R3pkp/P2p2pN/p1nPp1Q1/bn2P3/4P1NP/PBBPp1P1/5RK1 w - e6 0 1
The first time I saw this puzzle was at a site that gave the FEN above along with the board graphic. For several hours, I thought I had to be simply missing the right, normal move to mate in 1- it was driving me crazy, and began to suspect the the blog poster had simply played a cruel trick on his readers- that there was no solution. However, later that day, it suddenly occurred me that I might have overlooked an en passant move. However, when I looked at his FEN, it showed no en passant square in the notation, so I was again stuck. Later, when the blog poster revealed the answer was, indeed, dxe6 en passant, I pointed out to him that his FEN was not correct for the position. He explained that he didn't even know that FEN has a field for en passant moves, and that if he had known, he would not have included a FEN at all. Yesterday, when I creating the post, I had meant to omit the FEN altogether, but in my haste to get the post up, I thoughtlessly included it before I realized I had done so. That was why I wrote the first comment about ignoring it.
When I looked at the board I saw that it was impossible to solve it, but you said it was mate in 1. It meant that there was a trick in this puzzle. White must make a move which attacks the black king and h8. It's impossible to do if white doesn't take en passant.
That's how I solved it.
I won't ever reveal how long it took me to solve this the first time I saw it.