Score a Game of Boggle
Husk, 21 20 19 bytes
-2 bytes thanks to Zgarb
Idea taken from A055228
ṠṀöṁ(⌈√Π-3▼8L)fε`#Σ

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Explanation (Of older version)
            ṠṀ-oṠ-uΣ   Remove duplicated words
                   Σ   Concatenate
                  u    Remove duplicates
               oṠ-     Remove those unique elements from the list (give list of elements that appear more than once)
            ṠṀ-        Remove those words from each list in the input
m                      For each list
 ṁ(                    Map then sum
          L)           Length
        ▼8             Min(8,x)
      -3               Minus 3
     Π                 Factorial
    √                  Square root
   ⌈                   Ceiling