10. (12 points) Hxi and Shan each have several points cards.

Shan said to Hxi: "If you give me 2 cards, my number of cards will be twice yours."
Hxi said to Shan: "If you give me 3 cards, my number of cards will be three times yours."
Shan said to Hxi: "If you give me 4 cards, my number of cards will be four times yours."
Hxi said to Shan: "If you give me 5 cards, my number of cards will be five times yours."
It was later found that exactly two of the four statements are correct, and two are incorrect. In the end, Hxi gave Shan several points cards, and their numbers of cards became the same. How many points cards did Hxi originally have? $\qquad$
【Solution】Solution: Let Shan Shan originally have $x$ points cards, and Xi Xi originally have $y$ points cards. If all 4 statements are true, we can obtain the following four equations:
$$
\left\{\begin{array}{l}
x+2=2(y-2) \\
3(x-3)=y+3 \\
x+4=4(y-4) \\
5(x-5)=y+5
\end{array}\right.
$$

The last statement indicates that the total number of points cards between the two is a multiple of 2, and each person has a different number of points cards. Selecting 2 out of the 4 equations in order,

solving the system of linear equations and verifying the results, it is not difficult to find that only when the 2nd and 4th statements are correct can we get the right answer,
$$
\left\{\begin{array}{l}
3 x=y+12 \\
5 x=y+30
\end{array}\right.
$$

Solving gives: $\left\{\begin{array}{c}x=9 \\ y=15\end{array}\right.$
That is, originally Shan Shan had 9, and Xi Xi had 15.
Therefore, the answer is: 15