OMCC 2015 Problem 6

$39$ students participated in a math competition. The exam consisted of $6$ problems and each problem was worth $1$ point for a correct solution and $0$ points for an incorrect solution. For any $3$ students, there is at most $1$ problem that was not solved by any of the three. Let $B$ be the sum of all of the scores of the $39$ students. Find the smallest possible value of $B$ .