10. (15 points) Kangaroo A and B are jumping in the area shown in the figure. A jumps in the order of $A B C D E F G H I A B C \cdots$, and B jumps in the order of $A B D E G H A B D \cdots$. If both kangaroos start from $A$ and this counts as the first time they jump together, how many times have they jumped together after 2017 jumps?
【Analysis】First, find the least common multiple of the periods of 2 jumps, 6 and 9, which is 18. In this cycle, there are 2 meetings. Finding the number of groups and the remainder can solve the problem.

【Solution】According to the problem, we know:
By enumeration, the table is as follows:
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline Kangaroo A & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ & $H$ & $I$ & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ & $H$ & $I$ & $A$ & $\cdots$ \\
\hline Kangaroo B & $A$ & $B$ & $D$ & $E$ & $G$ & $H$ & $A$ & $B$ & $D$ & $E$ & $G$ & $H$ & $A$ & $B$ & $D$ & $E$ & $G$ & $H$ & $A$ & $\cdots$ \\
\hline
\end{tabular}

The cycle length is 18. There are two meetings in each cycle.
$$
2017 \div 18=112 \cdots 1 \text {. }
$$

Therefore, after 2017 jumps, the two kangaroos meet $1+2 \times 112+1=226$ (times);
Answer: After 2017 jumps, they meet 226 times.