I. Fill in the blanks (27 points)

1、

1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15

In the above table, each time two numbers are packed continuously, one * * * can get () different sums; Every time you type five numbers in a row, a * * * will get () different sums.

2. There are 18 consecutive movie tickets. You have to get 3 consecutive tickets, and there are () different ways to get them.

There are 15 different numbers in a * * * table. If there are 7 numbers in each box, a * * * can get () different sums; If you want to get 10 different sums, check () every time.

4. The first group of five classes (1) has 10 people queuing to carry out comprehensive practical activities. Xiaohong is next to Xiaoli in the queue. Xiaohong and Xiaoli have () different arrangements.

A cinema has 32 seats in a row. Xiaoming took his brother to the movies. Considering taking care of the younger brother, their seats must be adjacent. If Xiao Ming sits on his brother's left, there are () different sitting postures in the same row; If Xiao sits on the left or right of his brother, there are () different ways to sit in the same row.

6. There are tiles on one wall of the bathroom, and the six pieces in the middle form a pattern.

Under the condition of keeping the combination pattern unchanged, there are () different pasting methods.

Second, choose carefully (choose the serial number of the correct answer in brackets) (6 points)

1. There are 25 books in the middle of the bookcase. If three books are randomly selected, three books are required to be connected, and * * * has a () selection method.

a、22 B、23 C、2 1 D、24

There are 18 seats in a row in the auditorium. Xiao Fang and Xiaoying are twin sisters. Sitting in the same row, there are () different ways to sit together.

a、 17 B、 18 C、34 D、36

Three, independent exploration, hands-on operation (***29 points)

1 2 3 4

5 6 7 8

9 10 1 1 12

13 14 15 16

1, and on the right is a 4×4 square piece of paper, which is made up of 16 pieces of paper of the same size.

Square, write a number for each square.

(1) If one is removed from this square piece of paper, how many kinds of * * * are there?

Different roads to go?

(2) If the sum of the four numbers removed is 50, where should these four numbers be in the diagram? (color coding)

Day one two three four five six

1 2 3

4 5 6 7 8 9 10

1 1 12 13 14 15 16 17

18 19 20 2 1 22 23 24

25 26 27 28 29 30

2. The following is 10 copy of the desk calendar in 2006, marked "convex".

Typing boxes, 4 boxes at a time.

(1) If the minimum number of frames is 5, the number of frames is

What are these four numbers? What is the sum of them framed in the picture?

(2) How many different sums can a * * * frame?

This is the calendar of June of a certain year, and now we use "ten".

Font frames numbers in the calendar, five at a time.

(1) What is the minimum sum of boxes and what is the maximum sum of boxes?

How old?/How big?

(2) If the sum of the five numbers in the box is 105, what is the middle number?

(3) How many different sums can a * * * box produce?

Fourth, walk into life. (38 points)

1. My mother has a 7-day long holiday on National Day, and she wants to take Honghong to travel to Huangshan. Since this scenic spot is far away from Yancheng and needs to be visited for three days, how many different choices can there be?

My brother and younger brother go to the movies together. The cinema has 30 seats in each row. They sat in the same row, close together. How many sitting methods are there?

3. Yancheng Cinema has 28 seats in each row, * * * 19 rows. Xiao Gang and Xiao Ming went to the movies and asked them to sit together. How many different ways are there?

4. Arrange the natural numbers in the right order,

In this array, two straight lines are framed by rectangles.

Six numbers (the rectangular box in the figure is for illustration only), if

The sum of the six numbers in the box is 432, you know.

Six numbers in the upper left corner and the lower right corner of the box.

What's the total?