At first I thought it was a hoax at first but some after some cursory investigation it may not be. The email address that one is supposed to write to with a solution was only registered last year and at first I couldn’t find any Penrose Institute but I did find it eventually and it may all be legit because that site was only started last year too.
Where I saw the original story, then another more in depth story I found here…So, to the problem itself but I must admit I’m still a little suspicious.
Initial observations are thus. Black has no moves it can make other than the bishops and all three are on black squares so the white king is relatively safe on white squares. There seems to be some clues provided, the hand drawn chess board has an x diagonally beside the furthest white pawn. Significant? Perhaps. It also says below it that it’s easy for humans and that it is a ‘legal’ position. Amusing to say the least, here is some chatter on the forums at chess.com