11. (15 points) As shown in the figure, there is a circle filled with the number 1. Please fill in the blank circles with one of the numbers $2,3,4,5,6$, ensuring no repetition, and the difference between adjacent circles' numbers is at least 2. How many different ways are there to fill the circles?
【Analysis】We can analyze by finding the position according to the numbers, number 2 cannot be near 1, number 3 cannot be near 2, and we can enumerate based on the position of the numbers for analysis.

【Solution】Solution: The difference between the numbers in adjacent circles is at least 2. Let the letters in the figure be $a, b, c, d, e$. Therefore, 2 can only be filled in $d$ and $e$.
(1) Fill 2 in $d$, 2's surroundings cannot have 3. So 3 can only be filled in $a$. 3's surroundings cannot have 4, 4 can only be filled in $c$ and $e$. 5 and 6 cannot be together, so 5 is filled in $b$. 6 and 4 can be exchanged in $c$ and $e$, at this time there are 2 ways to fill; (see the middle figure)
(2) Fill 2 in $e$, 3 can be filled in $a$ or $b$.
If 3 is filled in $a$, 4, 5, 6 must have two adjacent, there is no way to fill that meets the condition;
If 3 is filled in $b$, 4 can only be filled in $c$, 5 can only be filled in $a$, 6 is filled in $d$.
1 way to fill; (see the right figure)
Therefore, there are $2+1=3$ ways in total.
Answer: There are 3 different ways in total.