D - Coloring Dominoes

  • image
  • Thoughts.
    • You are given a highly flexible representation of the placement of the dominoes, but essentially all you need is a “place them vertically” or “place two horizontally” column. Convert to that first.
    • when the foreground is horizontal
      • Verticals have only one way to paint.
      • The sides are three ways: ba, bc, and ca, with ab in the foreground.
    • when the foreground is vertical
      • Vertical is two ways
      • There are two sides, bc and cb, with a in the foreground.
    • The first three ways are vertical, and the sixth way is horizontal.
    • The rest can be calculated in any order.
    • Official Explanation OK

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