9. (12 points) 12 Smurfs are sitting around a round table, each Smurf hates the 2 Smurfs sitting next to him, but does not hate the other 9 Smurfs. Papa Smurf needs to send out a team of 5 Smurfs to rescue Smurfette who was captured by Gargamel, the team cannot include Smurfs who hate each other, then there are $\qquad$ ways to form the team.
【Solution】Solution: Divide into three major categories as required:
One category is to select all odd-numbered, the number of groups is $C_{6}^{5}=6$,
The second category is to select all even-numbered, the number of groups is $C_{6}^{5}=6$,
The third category is a mix of odd and even numbers, which is more complex and further divided into 4 subcategories:
1st category: 1 even 4 odd (or 4 odd 1 even), the groups formed are: 2-5-7-9-11, 4-7-9-11
2nd category: 2 even 3 odd (or 3 odd 2 even), the groups formed are: 2 - 4-7-9-11, 4-6-9-11-1, 6 - $8-11-1-3$, $8-10-1-3-5$, $10-12-3-5-7$, $12-2-5-7-9$ for a total of 6 types.
3rd category: 3 even 2 odd (or 2 odd 3 even), the groups formed are: 2 - 4 - $6-9-11$, $4-6-8-11-1$, $6$ $-8-10-1-3$, $8-10-12-3-5$, $10-12-2-5-7$, $12-2-4-7-9$ for a total of 6 types.
4th category: 4 even 1 odd (or 1 odd 4 even), the groups formed are: 2 - 4 - 6 - 8 - 11, 4-6-8-10-1, 6 $-8-10-12-3$, $8-10-12-2-5$, $10-12-2-4-7$, $12-2-4-6-9$ for a total of 6 types. According to the calculation method: $6+6+(6+6+6+6)=6+6+24=36$ (types). Therefore: There are a total of 36 methods to form teams.