Find a super difficult math problem, find a super difficult math problem

is in line 45, column 14.

Yes is set first to be in the nth row, and then according to the first number in each row.

The general formula for the first number of each line is 2 n(n-1), and then according to the law of each line, the difference is 2, and 2006 is the n number of the nth row, you can write 2 n(n-1)+(m-1)2=2006

This results in n=45 m=14

Note: n is calculated by assuming that 2006 is the first of the nth row, that is, n(n-1)+2=2006, and by bringing in n to take a natural number that is slightly smaller than 2006, and then determining the value of n, and then bringing in 2 n(n-1)+(m-1)2=2006 to calculate m

n is the number of rows. n*(n-1)+2 is equal to the first number of n rows.

Solution: n*(n-1)+2=2006, so that n is approximately equal to 45, and the first number in line 44 is 45*(45-1)+2=19822006-1982=24 24 2+1=13 columns.

At the end of the first row, number 1*2

At the end of the second row, number 2*3

At the end of line 44, 44*45=1980

The end of the 45th line is 45*46=2070

So 2006 in line 45, column 13.

Line 45 is the 13th, not the 26th, and the brother above forgot to divide 2

3rd? I'm terrible at math!

If you really want to go through reasonable steps to find it step by step, it is estimated that you must first learn the Chinese remainder theorem, which is quite troublesome knowledge of number theory, if you are interested, you can read it.

If you don't ask for such depth, it is. Let the total number of people x, then x=8k+5

k gradually increases from 1 to see which one satisfies the second one.

Obviously k = 1, x = 13

k=2, x=21

k=3,x=29

k=4,x=37

k=5,x=45

k=6,x=53

k=7,x=61

k=8,x=69=7*9+6 satisfies, so the total number of people is 69 If you don't agree with the above steps, it is estimated that you have to learn the Chinese remainder theorem.

Let a total of x people, 8 people have group A, 9 people have group B, and the column equation has x=8a+5=9b+6

8a=9b+1

Find the smallest integer solution.

b=7，a=8

At this point x=69

Find the least common multiple of 8 and 9 72

So the minimum is 69 people, and the total number of people may be 69+72k (k takes 0,1,2,3,。。

I guess the question is to ask you to ask at least how many people! That's an estimated 69 people!

There is a group of 8 people with X group and a group of 9 people with Y group.

Then 8x+5=9y=6, we get 8*(x-y)=y+1 (this problem should be the least number of people, then x is the smallest, y is the smallest).

Since the left side of the equation is a multiple of 8, then the right side is also a multiple of 8, that is, y+1 is a multiple of 8, and the smallest is a multiple of 8, then y=7, so the minimum number of people is 7*9+6=69 people. This method is logical for every step, the other answers are not very good, they are all patchwork, and this type of problem can be transformed into a multiple of a certain number on one side and an unknown number on the other.

It's simple: if the first division has m people, then m=8x+5

In the second division, there are n people, then n = 9y+6

x =1 2 3 4 5 6 7 8 9

m=13 21 29 37 45 53 61 69 77

y=1 2 3 4 5 6 7 8 9

n=15 24 33 42 51 60 69 78 87

So we know that the total number of people is 69

And because the least common multiple of 8 and 9 is 72, the total number of people can be 69+72k (k=0,1,2...).

In a group of 8 people, there are 5 people left, then there are a total of (8a+5) people (a is an integer and 0<=a<8); In a group of 9 people, there are 6 people left, then there are a total of (9b+6) people (b is an integer and 0<=b<9). Then 8a+5=9b+6, collated: 9a-9b=1+a, 9(a-b)=1+a.

Because 0 is less than or equal to a-b is less than or equal to 9, and 1+a must be a multiple of 9, so 1+a=9, get a=8, then the total number of people = 8 times 8 plus 5 = 69 people.

Because 8-5 = 3, 9-6 = 3. Let's assume that 3 more people join the game, and then the original question will be "8 people in a group is just right, and there is exactly no left in a group of 9 people." According to the least common multiple, it can be seen that there are at least 8 9-3 = 69 people in this group.

Let the total number of people z=8x+5=9y+6,x,y,z are all integers, then x=(9y+1) 8,x is an integer, then y is an odd number, and when y=1, x does not exist; When y=3, x does not exist; When y=5, x does not exist; y=7, x=8. So y1=7, x1=8, z1=, so yn-y(n-1)=8, xn-x(n-1)=9, zn-z(n-1)=72. So the total number of people is 72*n+69 (n=1,2,3...).

The answer is not unique, and the process is not easy to write (if it is an exam question). Suppose you can divide the group of nine people into x, and there are six people left, if you want to change the group of nine people to a group of eight people, then one person can be drawn from the group of nine, and x people can be drawn, then x+6 divided by 8 must be 5, then x+6 can be 13, 21, 29 ......So x=7,15,23....So the total number of people is 9x+6=69,141,267....

In a group of 8 people, there are 5 people left. If you are in a group of 9 people, and there are 6 people left, if you find 3 more people, 8 people, and a group of 9 people is just right.

Therefore, with x individual x+3 should be a common multiple of 8 and 9.

So x=72k-3 (k is an integer greater than or equal to 1).

Set up a total of x people.

Let x=8a+5=9b+6

8a=9b+1

Find the smallest integer solution.

b=7，a=8

At this point x=69

Find the least common multiple of 8 and 9 72

So the minimum is 69 people, and the total number of people may be 69+72k (k takes 1,2,3,。。

Feel free to ask questions.

There is a group of 8 people in the X group, and a group of 9 people in the Y group.

8x+5=9y+6

where x and y are positive integers, and the final verification is: x=8 y=7

Therefore, the total number of people is 69.

There is an X group of 8 people and a Y group of 9 people.

then 8x+5=9y+6

and y then x=(1+9y) 8

When y=7, it is divisible, x=8

Total enrollment: 69.

Reference).

If you assume there are n groups, then 8n+5=9n+6

You have a problem with this question: the answer is n=-1

This is a classic case of Han Xin's point soldiers! The answer is 69

1 2a squared.

Please believe in the strength of the senior high school students!

Uh, sorry.

Misunderstood. Such.

The small triangle in the upper left corner of the question is 1 3 of the area of the irregular quadrilateral, and then the last two figures can be spliced into a small positive in the middle.

Therefore, the area is 1 in the unit of the small triangle of Mill Xun

Then the proportion of small positives is 4 20

So the small positive area is 1 5a squared.

Four small triangles are the same size.

The small triangle row and the middle triangle are proportional triangles.

Because the side-to-length ratio is 1 to 2

So. The area of the small triangle is 1 4 of the area of the middle triangle, and the area of the middle volume of the small triangle is 1 5 of the triangle

And the area of the large triangle is 1 of the big positive, and the area of the 4 small square is equal to the area of the front angle of the four small three mountains.

So. s small positive = 4x1 5x1 4 = 1 5 major positive.

The front is talking about the cube, and the back is how to change the square. You mean square, the answer is no, it should be a quarter of a square. That's 1 4 of the square area. Li trembled.

I'll still answer it.,But I'm a junior now.,I've forgotten some theorems or something.,I vaguely remember a book of projective theorems or something.。

The area of this small cube is s=( 3 4*a) =3 16*a

Counted from the last person;

I know that he bought 1.

You can set her to buy x one.

x=x/2+1/2;x=1）；

So Xiao Zhang bought 2;

Aunt Liu bought it.

2 Uncle Li bought.

4 out of 9;

x-y=3

x-z=1 3, the second formula minus the first.

y-z=-8/3

I'm dizzy, use two formulas to subtract it, it's ok fun, and the rear formula minus the front style to get it.

y-z=-8/3

Subtract the two algebraic formulas to give y-z=-8 3

I think this topic is problematic :

1. After the encounter, B travels 951, A travels 857, B travels more than A2, B is slower than A, so it takes the second half of B's driving time more than A3, how to achieve that B travels more than A? Analyze the time t: from the encounter to the arrival of A at the end point B

t 5 hours, the minimum driving time of A is 4 hours for T-1, the maximum driving time for B is 4 hours, and the maximum time difference is 1 hour.

t>5, A's minimum driving time is 4+ T A, B's maximum driving time is 4+ T B T A》 T B, so: T B is impossible" T A.

4. According to the analysis of Article 3, under the premise that "B has more driving time than A", the maximum driving time of vehicle B is 4 hours.

5. Then, B needs to travel a distance of 951 (greater than half a distance) within a maximum of 4 hours6, comprehensive analysis, the whole process A and B take a break at least once, so B should have a break 7 before the encounter, and B's driving time before the break is at least 4 hours, but when they meet, B travels less than half the distance Conclusion 5 contradicts Article 7.

Discussion and correction are welcome.

It's easy to find that there is no solution to this problem.

The last hour of the 6 hours of A and B rest at the same time, so it can be omitted, that is, it is equivalent to A walks all the time, B walks for every 4 hours, rests for 1 hour, and in combination with the conditions, A is faster than B, then the distance traveled by B is 4 5 of the distance traveled by A, so it can be deduced When A arrives at place B, B's journey is 1844 4 5= contradicts the inscription Car B is 36 kilometers away from place A!

So there is no solution to this problem, or the data of the lz problem is wrong.

Set the meeting time to x, car A speed to y, car B speed to x

4y+2z=1844

4y-2z=65

1844/y=(1844-36)/z

xy+xz=1844

The first thing to do is to calculate the time to know the speed of the car.

Let the time of meeting x speed of A y speed z of the two vehicles meet and the distance traveled by A is 1844 2+65=987, and the distance traveled by B is 1844-987=857

xy=987

xz=857

1844 /y=（1844-36）/z

There are three situations that should be divided into three situations when encountering:

1. A moves and B does not move;

2. A moves and B moves;

3. A does not move and B does not move.

First of all, the first floor is right, the location of points A and B is not clear, is it a known condition? Or is there a picture for this question? Secondly, the one on the second floor is absolutely wrong!

If A starts in place A and B starts in place B, the distance traveled by A and B is 987,857 respectively before they meetAfter the encounter, the trip of A and B is 857,951. So there is something wrong with the topic itself.

Your point b and point a are known conditions???