9. Five pairs of twin siblings participate in the activities of $k$ groups. If the rules are: (1) Twin siblings are not in the same group; (2) Any two people who are not twins have participated in exactly one group together; (3) One person participates in only two groups. Then the minimum value of $k$ is $\qquad$
Let the five pairs of twin siblings be $A, a, B, b, C, c, D, d, E, e$. Since one person only participates in the activities of two groups, let's assume this person is $A$, and the members of the two groups $A$ participates in are $\{A, B, C, D, E\},\{A, b, c, d, e\}$. From (2), we know that except for the group that $a$ participates in, which can have a maximum of 3 people, the other groups can have a maximum of 2 people. The binary combinations of $B, C, D, E$ and $b, c, d, e$ total 12, meaning each person must participate in at least 3 groups. Therefore, the groups can be divided as follows: $\{a, B, c\},\{B, d\},\{B, e\} ;\{a, C, b\},\{C, d\},\{C, e\} ;\{D, b\},\{D, c\},\{a, D, e\}$; $\{E, b\},\{E, c\},\{a, E, d\}$, totaling 14 groups. Therefore, the minimum value of $k$ is 14.