Does b always mean prizes by ranking while a means the order of awarding?
a)I could have won the first prize
b)I could have won first prize.
A) could be either IMO- it's another one for the context.
[not a teacher]
Tdol means that one can't tell the meaning, without additional context (information surrounding the statements).
To me, I think you are correct, except I would remove "always", because context matters.
Last edited by BobSmith; 01-Feb-2012 at 12:22. Reason: Added my opinion on the OP.