9. (12 points) Hixi and Shanshan each have several points cards.
Hixi says to Shanshan: "If you give me 3 cards, my number of cards will be 3 times yours."
Shanshan says to Hixi: "If you give me 4 cards, my number of cards will be 4 times yours."
Hixi says to Shanshan: "If you give me 5 cards, my number of cards will be 5 times yours."
It is known that exactly one of the above three statements is incorrect. Therefore, originally Hixi had $\qquad$ points cards.
【Answer】Solution: According to the analysis, assuming the first and second sentences are correct, then the total should be a multiple of 20. According to the first sentence,

the ratio of Xixi to Shanshan's points cards should be 15:5, and according to the second sentence, the ratio of Xixi to Shanshan's card numbers should be 4:16, the difference of 11 times for each person corresponds to 7 cards, which is not an integer, so it is discarded.

Assuming the first and third sentences are correct, the total should be a multiple of 12. According to the first sentence, the ratio of the two people's points cards is $9:3$, and according to the second sentence, the ratio of the two people's points cards is 10:2, the difference of 1 part is the extra 2 cards, which is valid, so the ratio of Xixi and Shanshan's points cards is 6:24, according to the third sentence, the ratio of Xixi and Shanshan's points cards is 25:5, the difference of 19 parts is 9 cards, which is not an integer, so it is not valid, and is discarded.

In summary, the first and third sentences are correct, Xixi has 15 points cards.
The answer is: 15.