(The 2nd "Walking into the Wonderful Mathematics Garden" Grade 5 Competition)

2. The six-digit 2003 () () can be divisible by 99. What are its last two digits?

(The first "Hope Cup" National Invitational Tournament)

3. A three-digit ABC is multiplied by its reverse number CBA, and the product is a multiple of 2002. What is this multiple? (The 1st 1 1 Japan Mathematical Olympiad Final)

4.abc stands for decimal three digits. If abc is equal to the sum of all two digits consisting of three digits A, B and C, write all three digits that meet the above conditions.

(Final of the 10th "Huajin Cup" Junior Mathematics Invitational Tournament)

5. A three-digit natural number is exactly equal to 18 times the sum of its three digits. What is this three-digit number?

(The 10th "Zu Chongzhi Cup" Mathematics Competition)

6. The teacher quoted a four-digit number. After reversing the four digits, a new four digits are obtained. Add two four-digit numbers. The answer of A is 9898, the answer of B is 9998, the answer of C is 9988, and the answer of D is 9888. It is known that one of the four students A, B, C and D got the correct result, so who did it right?

(The 7th Zu Chongzhi Cup Mathematics Invitational Tournament)

7. There is a quiz, and the last level is to break through the "winning" gate. There are two doors, one is the door of life and the other is the door of death. After going through five and six levels, Xiao Qiang defeated several experts. He was the only one who won and passed the last level. As long as he can pass through the door of life in two doors, he will win the prize in the end. If he can't get through life, all his previous efforts will be in vain. The last level is like this: there is a soldier standing in front of these two doors. Both soldiers know which is the door of birth and which is the door of death. However, one of them always tells lies and the other always tells the truth. But Xiao Qiang didn't know which of the two soldiers was telling the truth and which was lying. He can only ask one of the two soldiers a question before choosing the two doors to pass through, so that he can decide to take one door (the two doors are exactly the same, without any mark).

8. Five couples, A, B, C, D and E, get together and shake hands when they meet. Mr. A curiously asked everyone (including his wife) the number of handshakes just now, and the answer surprised him. No two out of nine people will shake hands at the same time. How many times does Mrs. A shake hands (couples don't shake hands)?