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Sixth grade simulation test paper of Hope Cup Mathematics Invitational Tournament [1]
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1. In the following formula, the same Chinese character represents the same number, and different Chinese characters represent different numbers, and the sum is a multiple of 300.

Then, the five digits represented by "Zhejiang Olympic Mathematical Network" are at least.

2. There is a 1 digital card on the desk. A, B, C and D each took two.

A said, "The sum of the numbers of my two cards is 12."

B said, "The number difference between my two cards is 4."

C said, "The product of the numbers of my two cards is 12."

Ding said, "My quotient of two cards is 4."

So, the numbers on the remaining cards are.

3. Starting from 1, after the odd numbers arranged from small to large are divided by multiples of 5, the 2008th number is.

4. Someone shot 10 and hit 4 shots, of which just hit 3 shots in a row. There is a different situation.

5. The least common multiple of four consecutive odd numbers is 3 15, so the sum of these four odd numbers is.

6.a, B, C and D are non-zero natural numbers and satisfy the following formula.

7. The natural number 2008 has a divisor, and the sum of these divisors is.

9. Among the original 2008 natural numbers, one did not include the number 2.

10, there are twelve stairs, each level can go up to the first, second and third levels, and it is not allowed to step on the fifth and ninth levels. Then, there is a different road from the ground floor to the twelfth floor.

1 1. There are 59 white balls and 60 black balls of the same size in the pocket. A takes two balls out of his pocket at a time. If the two balls are the same color, B will find another black ball of 1 and put it in his pocket. If the two balls are different colors, B will put the white ball back in his pocket. B After operating 1 17 times, there was a white ball left in the pocket.

12, a store has Sprite liter, Coke liter and orange water liter; Put them into vials respectively, and the volume of liquid in each vial is the same, and there is no residual liquid. At least one small bottle must be prepared to complete the repackaging of these sprite, cola and orange juice.

Second, solve the problem (requirements: write out the calculation process)

13. There are 50 students in a class, among whom 20 can play basketball, 25 can play volleyball, 24 can play football, 7 can play basketball and volleyball, 9 can play volleyball and football, 8 can play basketball and football, and 3 can play all three kinds of ball games. How many people can't play three balls? How many people know only one ball game?

14. A teacher tested five subjects of five students, and the scoring method was quite special. The best score in all subjects is 1, followed by 2, 3, 4 and finally 5. After the test, the result is known:

(1) Total score ranking: E > D > C > B > A, everyone has a door that is the first;

(2) The total score of A is 12, and that of B is14;

(3) Comparing with each other, A has the best record in history; B Chinese is the best, and geographical English is the third; C has the best performance in geography, second in mathematics and third in history; Math first, English second. Please tell us about Ding's achievements in various subjects.

16, A and B are 26 kilometers apart. A and B walk from A to B at the same speed. Party A left for a few minutes, while Party C and Party B left A at the same time. After catching up with Party A by bike, Party C returned to find Party B. When he met Party B, he caught up with Party A and then returned to find Party B. When Party B and Party C left Party A, Ding walked from Party B to Party A. Ding met A and C on foot for 6 kilometers and caught up with A for the sixth time. When A went to B, C caught up with A for the eighth time. How many kilometers does Ding have left B at this time?