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Mathematical Olympiad Simulation of Grade Five in Guangdong Province (1)
The last two digits of1.761001+251001

2. Write the nine numbers 1 to 9 on a piece of paper, as shown in the figure, cut them into three sections, and connect the numbers in each section to work out a number. Add these three numbers together so that the sum is divisible by 77, so the number in the middle part is.

3. Many children line up. For the first time, from left to right, 1 ~ 3 counts off, and the rightmost child counts off 2. The second time from right to left, 1 ~ 5 counts off, and the leftmost child counts off 3. If four children signed up for 1 twice, then * * * has one child.

4. Ten digits, where different letters represent different numbers, A is a multiple of 1, two digits are a multiple of 2, three digits are a multiple of 3, and four digits are a multiple of 4 ... Ten digits are a multiple of 10, so these ten digits are.

Between 0: 00 and 12: 00, the hour hand and minute hand on the clock face are both 60? The angle is * * * times.

6. 10 players participate in the chess game, and every two players have to play the next game. The scoring method is to win a set of 1, draw a set of 0.5, and lose a set of 0. As a result of the competition, the players got different scores. The first and second place have never lost a set. The total score of the top two is more than that of the third 10. If the sum of the scores of the fourth place and the last four places is equal, the third place scores.

7. Of all the integers from 1000 to 10000, there are * * * that satisfy the increase or decrease.

8. In the triangle ABC, D is the midpoint of BC, E is the upper point of AB, and BE= AB. Given that the area of the quadrilateral BDME is 35, the area of the triangle ABC is.

9. Classify four-digit numbers with digits other than 0. The product of the first two digits of a four-digit number is added to the product of the last two digits. If it is odd, it is called class number; If it is even, it is called class B number. Class a numbers and class b numbers * * * have a.

10. Big trucks and cars start from the same place and drive along the same highway. The truck left first 1.5 hours, and the car caught up with the truck four hours later. If the car travels 5 kilometers per hour, it will catch up with the big truck in 3 hours after departure. How many kilometers does the car actually travel per hour?

1 1. The circumference of the circular runway is 500m, and Party A and Party B start from the starting point clockwise at the same time. A runs120m per minute, and B runs100m per minute. Both stop every 200 meters 1 minute. So, how many minutes does it take for A to catch up with B for the first time?

12. 12 Every child has a piece of luggage with the number 1, 2,3 ... 12, and every child uses a number tag to pick up his luggage. The luggage is arranged in a row according to the numbered order, and the children are arranged in a row at will, but only the luggage with the smallest number can be taken away, otherwise the children with luggage will be at the end of the queue (the children with luggage will no longer line up), and it takes one minute to count the number of people. The number plate inspection starts at four o'clock, and baggage No.3 is taken at four thirty-three and baggage No.8 is taken at four forty. Ask the children whose numbers are 1, 2, 3 and 8. What is the starting sequence number?

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