How to do this Olympiad problem 60, how to do this Olympiad problem

Impossible. Coloring this diagram at intervals like a chess board, with a total of 5 5 = 25 squares, assuming that the upper left corner is a black square, then it is easy to see that there are 13 black, 12 white, and the triangle is white. Then the circle has 13 blacks and 11 whites.

To connect all circles horizontally and vertically, it must be in such an interval order: black, white, black, white, if the start and end points are different colors, then the number of black and white is the same, if the start and end points are the same color, then the difference between black and white is 1. The number of circles in this diagram is 2 different from black and white, so it is impossible to connect all of them according to the method given in the question.

The law is that any graph with even or at most two odd dots can be connected in one stroke. These are simple problems of topological math.

The so-called odd-numbered point: any vertex on the graph, if there is an odd number of lines connected to it, is an odd-numbered point, otherwise, it is an even number. Note:

Odd dots can be present or none, but there can be only two at most, and there are many graphs with two odd dots. It can't be linked in one go. )

For example, squares are all even-numbered points.

Not possible. There must be a point that is repeated.

If you start from one in the middle, you can't solve the first row of the first one, only end here, what's the difference between that and starting here?

Euler has already told us that this can't be connected, and no one will connect if you give 30,000.

Fold the paper and connect it.

There is no solution to this problem: mathematician Euler's "one-stroke drawing" problem gives a similar solution, see for yourself!

Sisha is the correct solution, Dongfang Hong's picture has an extra row of circles, is it trying to fool the pass.

After the first day of repair, there is still the following:

480+10) (1-2 9) = 630 meters Overall length: 630 (meters.

Composite formula: 480+10) (1-2 3) (m.

+[ 2 9)+10 ] = x-480, that is, the sum of the first day of repair and the second day of repair is x-480; You can solve x and calculate it yourself.

Three kinds of fruits in total: (52 + 48 + 56) 2 = 78 kg pears: 78-52 = 26 kg.

Oranges: 78-48 = 30 kg.

Apples: 78-56 = 22 kg.

I think it might be like this, cut the left side the way, move the left half of the block to the right, and get the right figure, so that there are two triangles.

Tangerine + Apple - (Apple + Pear) = Tangerine - Pear = 52-48 = 4 Tangerine - Pear + (Tangerine + Pear) = 4 + 56 = 60

Tangerine Tangerine = 60

Oranges = 30, apples brought in = 22 and pears = 26

The price was reduced by 6 yuan.

Make an equation and it's done, let the number of spectators at the beginning be a (in fact, if you figure it out, you can also set it, it can be understood as a change in ticket prices, which will be said later) After the price is reduced, the ticket ** is p, then:

2pa=15x（1+20%）a

The solution is p=9, so the price is reduced by 6 yuan.

In fact, it's very simple to figure it out, the number of spectators is useless, and then the audience doubled, but the price was reduced, which can be understood as the same as the number of spectators at the beginning, the ticket price (is the price multiplied by 2 after the price reduction) became the original 120%, that is, 18, so the ticket price after the price reduction is 9, and it can be reduced by 6 yuan.

Orange + apple = 52, apple + pear = 48

Orange + pear = 56

Add the three formulas, 2 (orange + apple + pear) = 156

Orange + apple + pear = 78

Subtract the first formula, get.

Pears = 78-52 = 26

Apples = 48-26 = 22

Tangerine = 56-26 = 30

The total weight of the three fruits: (52 + 48 + 56) 2 = 78 kg Apple: 78-56 = 22 kg.

Oranges: 78-48 = 30 kg.

Pears: 78-52 = 26 kg.

Solution 1, let a total of x trees and y willow trees.

y=x*2/5

y+50=(x+50)*5/11

Solution x=500

y=200 solution 2, let the total number of original x trees, x*2 5+50=(x+50)*5 11

Solution x=500

Solution 3, Proportional Algorithm:

2+x)/(5+x)=5/11

x = total number of trees.

Total number of trees = 500

52 + 48 + 56 = The total weight of the three fruits is 78 kg.

The weight of the pear: 78-52=26kgOrange weight: 78-48=30kgApple weight: 78-56=22

Ask for points.

52 + 48 = 100 is the weight of an orange and two apples and a pear;

And because oranges and pears weigh a total of 56 kilograms.

So 100-56=44 is the weight of two apples.

So an apple weighs 22 kg, an orange 30, and a pear 26

Column a ternary equation with apples xkg, oranges ykg, and pears zkgx+y=52

x+z=48

y+z=56

The solution is x=22

y=30z=26

It is known that there are 22kg of apples, 30kg of oranges, and 26kg of pears

Solution: Set orange xkg apple ykg pear zkg

From the title: x+y=52

y+z=48

x+z=56

The solution is x=30, y=22, z=26

Orange + apple = 52

Apple + pear = 48

Orange + pear = 56

Add the three formulas together to get:

Apple + orange + pear = (52 + 48 + 56) 2 = 78 in the subtraction of the above three formulas respectively to get :

Apples: 78-56 = 22 kg.

Oranges: 78-48 = 30 kg.

Pears: 78-52 = 26 kg.

It is not easy to answer the question, if you are dissatisfied, please understand

The ratio refers to the yuan person!

Then the money donated by all the people in class six (1) is 50 2+30 5+20 4+15 8+10 20+5 6 680

Then the money donated by all the people in class six (2) is 100 1+50 1+40 3+20 6+15 10+10 18+5 8 760

The total number of students in class six (1) is 2+5+4+8+20+6=45 people, and the total number of students in class six (2) is 1+1+3+6+10+18+8=44 people (680 45):(760 44)=748 855, that is, the ratio is.

。。Is this an Olympiad problem? That's it, the average donation amount is equal to the number of donations 5 times the number of people divided by the total number of people.

What is the ratio of the average donation per student? What does it mean.