(16x16) n1bqkbr1 - rpppppp1 - p6p - 8 - 8 - P4n1P - 1PPPPPPN - 1RBQKBRN
Is this a legal check?
Solution:
White is now in check, hence Black moved last. It's impossible!
When both sides has made the same number of moves, even or odd, then the
next move is white. If White has made an odd number of moves and Black even,
or vice versa, then the next move is black. The square's colors help us to
determine how many moves the piece on it has made and, after sum, how many
moves each side has made.
White:
a3=Odd, h3=Odd, 
b1=Odd,
g1=Odd, 
h2 plus h1=Even.
Total=Even. Black: a6=Odd, h6=Odd,
h7=Odd, g8=Odd, h8 plus
f3=Odd. Total=Odd. Then the next move is black and the
position is illegal.
My first problem after has knowed Retrograde Analysis in the Raymond Smullyan's The Chess Mysteries of Sherlock Holmes.