Roll a standard pair of six-sided dice, and note the sum.  There is one way of obtaining a 2, two ways of obtaining a 3, and so on, up to one way of obtaining a 12.  Find all other pairs of six-sided dice such that:

  1. The set of dots on each die is not the standard {1,2,3,4,5,6}.
  2. Each face has at least one dot.
  3. The number of ways of obtaining each sum is the same as for the standard dice.
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