Explanation
Alex Y
Bill got the right answer fairly quickly. But let me post the logic, so when I post another puzzle like this one, you will see the process.
A king can move one space at a time, in any direction. And the kings of each side cannot be on adjacent squares. Therefore, the only place the black King could have come from on the last move is the space immediately below where it is in the picture.
Before the Black king was moved, he was in check from the Bishop on the bottom row. But how did White put Black in check? The only place that bishop could have moved from is another place on the same diagonal, meaning Black was already in check. And because I specified which side was which, the bishop could not have been another piece promoted to a bishop. The only other possibility is that there was another piece previously blocking the attack from the bishop on the black king, and that piece got moved out of the way. No white piece on the board could have blocked that diagonal. The only possibility was a white knight which moved from the diagonal to the spot on the top row, where the Black king captured it. This is the (k)night in white satin reaching an end that Bill referred to.