Once upon a time, there was a very clever businessman. Once, he bought a horse at Mashihua 10 and sold it for 20 taels. Then, he bought it at 30 Liang, and finally sold it at 40 Liang. How much money did he make in this horse racing deal?

Reference answer:

This business can be divided into two parts. I bought 10 silver for the first time, sold 20 silver, and earned 10 silver. I bought 30 taels of silver for the second time and sold 40 taels of silver, so I also earned 10 taels of silver. In the horse trade, the merchant made 20 taels of silver.

number of people

Xiao Liang walked into the classroom and saw that there were only eight students in the classroom. How many students are there in the classroom now?

Reference answer:

The careless child thought there were eight classmates when he saw the topic, but the answer was wrong. After careful examination, they can find that "Xiao Liang entered the classroom", so the number of students now should include Xiao Liang, so there are nine students in a * * *.

Snail climbing well

A snail climbed a well with a depth of 10 meter, climbed 5 meters during the day and slipped 3 meters at night. When can snails climb out of the wellhead?

Reference answer:

Snails climbed 5 meters during the day and dropped 3 meters at night. In fact, it can only climb 2 meters every day. It took three days for the snail to climb 6 meters before, and there are 4 meters left, and it can climb out on the fourth day.

run quickly

Small animals hold animal games. In the long-distance race, four animals run in front of the little squirrel and three animals run behind the little squirrel. How many animals take part in the long-distance race?

Reference answer:

In order to find out the crux of this problem, we can regard all the running animals as a queue. There are four small animals in front of the squirrel and three small animals behind it. There are no squirrels in this queue, so we need to add little squirrels to the total number of this team. 4+3+ 1=8 (only), a * * * there are 8 animals participating in the long-distance running.

Count radishes

The little gray rabbit has 10 radishes. If the little white rabbit gives the little gray rabbit three radishes, they have as many radishes. How many radishes does the white rabbit have?

Reference answer:

If the white rabbit gives the gray rabbit three radishes, their radishes are the same, which is 13 for a long time. To get the white rabbit's original radish, you have to add it to the three radishes of the gray rabbit, so it is 16.

Interesting problems of natural sequences

Most of the exercises in this lesson are about the counting of natural sequence. The thinking methods to solve problems are generally enumeration and classified statistics. I hope the students can master it well.

Example 1 Xiaoming wrote 1 00 from1. How many numbers did he write "1"?

Solution: Classification calculation:

The number of "1" appearing in the cell is:

1, 1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,966.

"1" appears in the tenth digit:

10, 1 1, 12, 13, 14, 15, 16, 17, 18,666.

The number of "1" in the hundreds is:100 * * *1;

* * * 10+ 10+ 1 = 2 1.

Example 2 A picture book is *** 100 pages. When typesetting, a font can only arrange one digit. Please calculate how many fonts are used in the page numbers of this book.

Solution: Classification calculation:

From page 1 to page 9, * * 9, each page uses 1 type, * * uses 1×9=9 (pieces);

From page 10 to page 99, * * 90 pages, each page uses 2 kinds, * * uses 2×90= 180 (pieces);

On page 100, only three types are used on page 1 * *, so the total number of types used on page 100 is:

9+ 180+3= 192 (pieces).

Example 3 Write all natural numbers from 1 to 100. What is the sum of all the numbers used?

Solution: (See Figure 5- 1) First, write all natural numbers from 1 to 100 according to the meaning of the question, and then calculate them by classification:

As shown in figure 5- 1, there are single digits in the wide and vertical stripes, with 10 * *, and the sum of the digits is:

( 1+2+3+4+5+6+7+8+9)× 10

=45× 10

=450。

In the narrow vertical bar, each bar contains a ten-digit number with nine * * *, and the sum of the numbers is:

1× 10+2× 10+3× 10+4× 10+5× 10+6× 10+7× 10

+8× 10+9× 10

=( 1+2+3+4+5+6+7+8+9)× 10

=45× 10

=450。

In addition, the sum of the numbers 100 is 1+0 = 1.

So, the sum of these 100 natural numbers is:

450+450+ 1=90 1。

By the way, please note that a math problem often has more than one solution. Who can find and find a simpler solution often indicates who has stronger mathematical ability. For example, there is a simpler solution to this problem. Just try it. Can you find it?