Why did I ask a question in the sixth grade of primary school, and 4,921 people saw it, but none of

This is a deceptively simple question, but many people have tried and failed to find the answer. Therefore, a group of university students wrote to the great mathematician Euler, who was only 20 years old at the time, and asked him to analyze it. From the failures of thousands of people, Euler guessed with deep insight that it may not be possible to walk all seven bridges at once without repeating them.

To prove this conjecture correct, Euler used simple geometry to represent land and bridges. Here's how he solved the problem: since the land is the connecting point of the bridges, it is better to think of the land separated by the river in the diagram as four points A, B, C, and D, and the seven bridges are represented as seven lines connecting these four points, as shown in the figure "Seven Bridges Connecting Lines".

Simplified diagram of the seven-bridge connection line and then simplified it into a graph, which becomes the "simplified diagram of the seven-bridge connection" on the right. Before talking about Euler's inference, let's talk about the problem of even points and singularities. Odd and even dot diagram What is an even dot?

A point is even if it has an even number of edges. Points a, b, e, and f of the "odd and even dot diagram" below. Conversely, if a point has an odd number of sides, it is a singularity.

Euler believes that if a picture can be drawn in one stroke, then there must be a starting point and an end point. The other points on the map are "crossing points" – you have to pass through them when you draw them. What are the characteristics of "crossing points"?

It should be a point of "entering and exiting", and if there is an edge entering this point, then there must be an edge out of this point, and it cannot be that there is no entry and no exit or there is no entry and exit. If there is only in and no out, it is the end; If there is no entry or exit, it is the starting point. Therefore, the total number of edges in and out of the Crossing Point should be an even number, i.e., the Crossing Point is even.

If the starting point and the end point are the same point, then it is also a point that "enters and exits", so it must be an even point, so that all the points on the graph are even points. If the start and end points are not the same point, then they must be singularities, so this graph can only have a maximum of two singularities. To sum up what is said above, it is simply as follows:

There are only two types of shapes that can be drawn in one stroke: one is that all the dots are even. The other type is a graph with only two singularities.

Now compared to the diagram of the seven-bridge problem, let's go back and look at Figure 3, the four points A, B, C, and D are all connected by three sides, which are odd-numbered sides, and there are four in total, so this diagram must not be drawn in one stroke. Euler's study of the "Seven Bridges Problem" was the beginning of the study of graph theory, and at the same time provided a primary example for the study of topology. In fact, this kind of one-stroke painting game has been circulating among Chinese folk for a long time, and from long-term practical experience, people know that if all the points of the picture are even points, they can choose a point as the starting point and draw it in one stroke.

If it is a figure with two singularities, then choose a singularity as the starting point to finish it smoothly in one stroke. If you don't believe it, you can try the "odd and even dot diagram" in the picture above, choose C and D two singularities to draw, and you will definitely be able to draw it in one stroke. It's just a pity that for a long time, people have only regarded it as a kind of interesting game, and have not paid attention to it, and no mathematicians have summarized and studied it, which cannot but be said to be a pity.

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It's either too difficult, or it's too troublesome and lazy.

Three-sevenths more goats than sheep (number of sheep) x three-sevenths = (number of goats more than sheep).

Number of sheep x (1+3 7) = number of goats.

93 2=186 means that 6 cows and 16 sheep eat a total of 186 kg of grass, and 186-165 is the grass eaten by 6 cows and 16 sheep minus the grass eaten by 5 cows and 15 sheep, which is the grass eaten by a cow and a sheep in a day!

You have answered this question very carefully, but why do you use 93 2=186 and then 186-165?

3 cows and 8 sheep eat 93 kg of grass, 93x2=186 is the grass that 6 cows and 16 sheep eat. 186-165 is the grass eaten by a cow and a sheep.

Between two quantities, one quantity (change), the other quantity also follows (change), they are two quantities related, as long as the two quantities, (division relation), the ratio (certainly) is proportional relationship.

Two related quantities, one expands and the other shrinks, (multiplicative relation), as long as their product (certainly) is inversely proportional.

Additive or subtractive relationship, disproportionate.

Is it true that one quantity between two quantities increases, and the other quantity also increases, and they are two quantities that are related, and as long as there are two quantities, (division relation), the ratio (certainly) is proportional to each other?

That's right. Is it true that two related quantities increase in one quantity and decrease in the other, (multiplicative relation), as long as their product is (certainly) inversely proportional?

That's right. So if it's an addition or subtraction relationship, what is the relationship?

If it is an additive or subtractive relationship, it is disproportionate.

One quantity changes with the other, it is said that the two quantities are related quantities, for example, the pressure is high when the exam is approaching, hehe.

If the product of two quantities is constant, then one of them will get smaller as the other gets bigger or bigger as it gets smaller, then we say they are inversely proportional.

If the quotient of two quantities is fixed, then one of them will grow larger as the other grows larger, or smaller as it gets smaller, we say that they are proportional.

Additive or subtractive relationship, disproportionate.

The first does not say that the same multiple of expansion is not proportional, and the second does not say that the multiple of expansion and contraction are the same, and if it is addition or subtraction, it is not proportional or inversely proportional.

The first two are true, and the last addition and subtraction are disproportionate.

The meaning is pretty much the same, but it's not accurate enough, and you have to look at the concept specifically.

The first answer: (240+360) 8=600 8=75, so he should process 75 parts in an hour.

Second answer: total weight of apples = 110 30 = 3300 kg; The first class occupies 6 (6 + 3 + 2) = 6 11, weight = 3300 6 11 = 1800 kg; second class accounts for 3 11, weight = 3300 3 11 = 900 kg; The third class accounts for 2 11, weight = 3300 2 11 = 600 kg. Thank you for adopting

In addition, if you want to successfully practice and go to Elysium in this life, you can refer to the [Diamond Sutra Handout] of Master Jingkong on YouTube

Bag A gives bag B 5 kg, indicating that they are originally 5 2 = 10 (kg) A is 6 5-1 = 1 5 more than bag B

The corresponding quantity is divided by the corresponding fraction, 10 1 5 = 50 (kg) This is the unit "1" - the weight of B, and then find the bag A as 50 6 5 = 60 (kg) Got it, give more points! This is the primary school score focus. Unit one figured out.

Let the original weight of A be 6 kg and B weigh 5 kg, then 6 -5 = 5 + 5, so = 10, so A weighs 60 kg and B weighs 50 kg.

A is 6 5-1 = 1 5 more than B

A is 5 2 = 10 kg more than B.

Bag B of rice weighs 10 1 5 = 50 kg.

A bag of rice weighs 50 + 10 = 60 kg.

Armor bag: (6 5-1) 2 = 1 10 5 (1 10) = 50

B: 50 5*6=60

Sorry, the computer doesn't understand, so-so typed out, hope, thank you.

Solution: If bag A of rice x kg, then bag B of rice 5 6 kg.

x-5=5/6x

x-5/6x=5

1/6x=5

x=30

B bag: 5 2 (6 5 1) = 50 (kg).

Armor bag: 50 6 5 = 60 (kg).