(evaluation time: February 2, 200711:00—12: 00; 150)
First, fill in the blanks (each question 10, ***60)
1. Calculation: 12345×2345+2468×38275=
The 2008 Olympic Games was held in Beijing. The five Chinese characters "Ao", "Yun", "Hui", "North" and "Jing" represent five continuous natural numbers, which are filled in the five rings of the five-ring pattern respectively, satisfying =. The maximum sum of these five natural numbers is
3. The electronic numbers 0 ~ 9 are shown in figure 1. Figure 2 is a multiplication formula composed of electronic numbers, but there are some ambiguities. Please restore the electronic numbers in Figure 2 and write them in the form of horizontal lines:
As shown in the picture, a 4×4 square is divided into five pieces. Please fill in one of 1, 2, 3 and 4 in each box, so that the four numbers in each row and column are different, and the sum of the numbers filled in each block is equal. Then, the sum of four numbers in A, B, C and D is
There are 35 books on a bookshelf, including math, Chinese, English and history. The number of each book is different. Among them, math books and English books 16, Chinese books and English books 17. There is a kind of book with exactly nine books. This kind of book is _ _ _ _ _ _ _.
There are three red balls, four yellow balls and five white balls in six bags. Xiaoming took six balls from them at random. It is possible that he took the ball out.
Two. Fill in the blank 2 (each question 15, ***90)
Xiaoming and Xiao Liang play poker. Each of them has a card with points of 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. They play a card in each round, and the one with more points wins. /kloc-after 0/0 round, what is the maximum sum of the total scores of the two players?
8 There are 100 cubes with side length of 1cm, all of which are white faces, and 25 cubes with side length of 1cm, all of which are blue faces. Glue these 125 cubes together to form a big cube. The surface of a big cube is white, and its area is at least square centimeters.
9 A basketball player participated in 10 game, and he scored 23 points, 14 points, 1 1 points and 20 points in the 6th, 7th, 8th and 9th games respectively. His average score in the first nine games is higher than that in the first five games. If he scores in 10 game,
10 A string of natural numbers 1, 2, …, 98, 99 is written on the paper. One operation is to cross out the first three numbers in this column, and then write the sum of these three numbers at the end of the series. For example, after the first operation, you get 4, 5, …, 98, 99, 6; After the second operation, we get 7, 8, …, 98, 99, 6, 15. At this rate, there is only one number left. Add the first 99 numbers and the numbers written down later, and the sum of all the numbers appearing on the paper is
1 1 Put the pieces in the "8×8" grid, and each grid can hold at most 1 piece. If the number of chess pieces with 8 rows, 8 columns and 30 diagonal lines (as shown in the figure below) is required to be even. Then you can put a chess piece in the square of "8×8" at most.
12 As shown in the figure, a rectangle is divided into three parts: A, B and C, where both B and C are rectangles, and the side lengths of eight sides of A are 1, 2, 3, 4, 5, 6, 7 and 8 cm respectively. Then the sum of the areas of b and c is at most square centimeters. (Schematic diagram is out of proportion)