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What does it mean for a constraint problem to be over constrained?

  • A.The domains have been reduced to a single value each
  • B.No assignment satisfies all the constraints
  • C.Every variable appears in more than one constraint
  • D.The constraints are more numerous than the variables

Answer: B

An over constrained problem has no solution, and the practical response is usually to relax some constraints or to seek an assignment violating as few as possible, which turns it into an optimisation. Constraint counts and domain sizes are not the criterion, and multiple membership is normal. Recognising that a real problem stated as insoluble usually needs its requirements reconsidered, rather than a better solver, is the practically important response.

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