open-ended

[oh-puhn-en-did]
adjective
1.
not having fixed limits; unrestricted; broad: an open-ended discussion.
2.
allowing for future changes, revisions, or additions: open-ended agreements.
3.
having no fixed answer: an open-ended question.

Origin:
1815–25; open + end1 + -ed3

open-endedness, noun
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
open-ended
 
adj
1.  without definite limits, as of duration or amount: an open-ended contract
2.  denoting a question, esp one on a questionnaire, that cannot be answered "yes", "no", or "don't know"

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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Etymonline
Word Origin & History

open-ended
1825, from open + end.
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
For everyone else, the system would no longer be an open-ended one in which the
  government paid for unlimited medical care.
Go look it up, and then tell me again that the benefit of having tighter
  control is an open-ended question.
Ask open-ended questions that allow her to talk about these things.
It is an intentionally open-ended story, prematurely closed, a mystery without
  a single solution.
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