Use of any in front of a singular noun
Solution 1:
any means any number--one selected or whatever quantity. Merriam Webster: A : one or more —used to indicate an undetermined number or amount Do you have any money?
So they won't win a trophy for coming in first, they won't win a trophy for being the tallest boys, they won't win a trophy for being the nicest boys, they won't win any trophy.