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Fun Sports $(FS)$ provides training in three sports-Gilli-danda $(G)$, Kho-Kho $(K)$, and Ludo $(L)$. Currently it has an enrollment of $39$ students each of whom is enrolled in at least one of the three sports. The following details are known:

  1. The number of students enrolled only in L is double the number of students enrolled in all the three sports.
  2. There are a total of $17$ students enrolled in $G$.
  3. The number of students enrolled only in $G$ is one less than the number of students enrolled only in $L$.
  4. The number of students enrolled only in $K$ is cqual to the number of students who are enrolled in both $K$ and $L$
  5. The maximum student enrollment is in $L$.
  6. Ten students enrolled in $G$ are also enrolled in at least one more sport.

What is the minimum number of students enrolled in both $G$ and $L$ but not in $K$?

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