1、 Problem description
The problem of planting is actually very simple. The research of planting trees is on the way. Of course, most students can think of it here, but in the public examination, how to check the seemingly simple problem, what needs to be paid attention to, and how to deal with the problem of planting trees are the issues we need to be concerned about. According to the test questions, the problem of tree planting mainly studies the relationship between the number of trees and the distance of the road.
Second, classification of problem types
In terms of afforestation, there are two main situations, one is to plant trees in a straight line, the other is to plant trees in a closed ring line. First, let's look at the first type:
1. Linear tree planting
If you plant trees in a straight line, let's look at the relationship between the number of trees and the distance of the road. for instance.
For example: on a 100 meter long road, how many trees do you need to plant, only on one side, every five meters, and at both ends of the road?
So this is a problem, many people may just intuitively divide 100 by 5, but it's a mistake. This problem, 100 meters in total, is too much to imagine that we come from less, such as two trees, three trees will have two distances, four trees have three distances, and so on, we will find that the number of trees is always more than the number, in this case, we have this sample, 100 meters in total, 5 meters each tree, 100 divided by 5 equals 20, and the calculated distance is 20, The number of trees exceeds a distance of 21.
Conclusion: the number of trees planted on the straight road is 1 more than the distance.
2. Tree planting around
If you plant a tree on a closed loop, it's the same as planting a tree on a straight line, or if there's any difference we should notice, let's see.
For example: on a 100 meter long ring road, how many trees does it take to plant a tree every 5 meters?
The problem is the same as before. The only difference is that there are two distances between the straight road and a sealed ring road and the number and distance of trees we will analyze. There are two distances between two trees, three trees have three distances, and four trees have four distances. Similarly, we will get another conclusion. When the ring road is closed, the number of trees and the number of distances are equal, The problem is that dividing 100 by 5 is equal to 20, 20 trees. The number of distances is the same as the number of trees, that is, 20 trees.
Conclusion: the number of trees is equal to the distance on the closed road.