Like a question with many possible answers (4-5)

I believe the answer is:

open-ended

(Other definitions for open-ended that I've seen before include "Allowing free debate with no set time to finish." , "With no fixed limit, not circumscribed" , "Having no predetermined limit" , "Without fixed limits or restrictions" , "Having no fixed limit, perhaps a discussion" .)

I've seen this clue in the USA Today.

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