10. As shown in the figure, four small plates $A$, $B$, $C$, and $D$ form a ring, with some candies placed in each plate. Each time, you can take all the candies from 1, 3, or 4 plates, or from 2 adjacent plates. How many different maximum quantities of candies can be taken out? Please explain your reasoning. (15 points)
$10 \quad 13$
Solution: The maximum is 13. Because there are 4 ways to choose 1 plate; there are also 4 ways to choose 3 plates (i.e., 1 plate is not chosen); there is only 1 way to choose 4 plates; choosing 2 adjacent plates, after the 1st plate is chosen (in a clockwise direction), the 2nd plate is also determined, so there are also 4 ways to choose, totaling $3 \times 4+1=13$ ways.
Scoring reference: See the solution process; if only the correct answer is given without the process, only 5 points are awarded.