Discard and lead the right cards

John Buchan, a Scottish politician and novelist, whose most famous book was The Thirty-Nine Steps said, Every man at the bottom of his heart believes that he is a born detective."

It helps if a bridge player is a detective, uncovering clues from the bidding and play. But another word in that sentence is important in today's deal.

South is in three no-trump. West leads the spade queen. Given that the defenders can take only four tricks in spades, how should declarer plan to win the last nine?