11. A and B have a total of 22 candies in four different colors, and

the number of yellow candies is the largest. A and B take turns picking candies according to the following rules until all the candies are taken: B starts, and B takes two candies each time (or the last one), then A takes one candy of each color from the remaining candies. After all the candies are taken, A and B find that they have taken the same number of candies. Find the maximum and minimum values of the number of yellow candies at the beginning.
11. 16 and 8.

Since there are initially 22 candies, in the end, A and B each take 11 candies.

On the one hand, to maximize the number of yellow candies initially, according to B's selection method, B must take two yellow candies each time for the first five selections, and one yellow candy in the last selection. Since B makes a total of six selections, A should select 11 candies in five selections from the four colors. At this point, A's selection method is $11=4+3+2+1+1$.

On the other hand, B must make six selections. To minimize the number of yellow candies initially, A should take one candy of each color in five selections after B's selections, meaning A must take one yellow candy in each of the five selections $(11=4+3+2+1+1)$, and B must take one yellow candy in each of the last three selections. Let $A, B, C, D$ represent the four colors, where $A$ is yellow. The method for A and B to take the minimum number of yellow candies initially is:
$$
\begin{array}{l}
(D D, A B C D) \rightarrow(C C, A B C) \rightarrow(B C, A B) \\
\rightarrow(B B, A) \rightarrow(A B, A) \rightarrow(A,-),
\end{array}
$$

At this point, the number of candies of color $B$ and color $A$ is the same, which does not match the problem statement;
$$
\begin{array}{ll} 
& (D D, A B C D) \rightarrow(C C, A B C) \rightarrow(B C, A B) \\
& \rightarrow(B B, A) \rightarrow(A A, A) \rightarrow(A,-) \\
\text { or } & (D D, A B C D) \rightarrow(C C, A B C) \rightarrow(B B, A B) \\
& \rightarrow(B B, A) \rightarrow(A A, A) \rightarrow(A,-) .
\end{array}
$$

After verification, this matches the problem statement.