"At the same time, it is a great puzzle how the elementary principle escaped the Prime Minister and the Home Minister..."
Does not the posed puzzle itself have a simple/elementary in-built 'resolution'!: That the puzzle is so elementary that it cannot be rightly or reasonably expected 'not to escape' them !!
Does not the posed puzzle itself have a simple/elementary in-built 'resolution'!: That the puzzle is so elementary that it cannot be rightly or reasonably expected 'not to escape' them !!