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Why are carry variables introduced in a cryptarithmetic model?

  • A.They reduce the number of the letters that must be assigned
  • B.They are required by the all different constraint
  • C.They allow the puzzle to have more than one solution
  • D.They make each column constraint local rather than global

Answer: D

Without carries the addition relates every column at once, but with them each column involves only its own letters and two carries, so propagation works locally and effectively. The variable count rises, which is a price worth paying. All different is independent, and solution count is a property of the puzzle. Adding variables to reduce the arity of constraints is a counter-intuitive but standard modelling move, since propagation strength usually matters more than problem size.

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