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Single digit, 1+2+......9=45
Two digits, from 10 to 99
The ten digits appear 10 times from 1 to 9, i.e. 10 to 19 ,......90 to 99, so a total of 10*(1+2+......9)=450
If 0 is not counted, then 1 goes from 11, 21, to 91, 9 times.
then the others are also 9 times.
So it's 9*(1+2+......9)=405
So the two-digit number is 450 + 405 = 855
Three digits. hundreds, 1 from 100 to 199, 100.
So the others are also 100 pcs.
So it's 100*(1+2+......9) = 4500 decimal digits, 1, is 110, 111 ,......119,210,……919 appears 10*9=90 times.
So the sum of the ten digits is 90*(1+2+......9) = 4050 digits, 1, from 101 to 991, is 90.
So the single digits are a total of 90 (1+2+......9) = 4050, so the same goes for the three-digit number 4500 + 2 * 4050 = 12600. Four digits, the thousand digits are 1000*(1+2+......9) = 45000 hundreds, ten digits and single digits are 900*(1+2+......9) = 40500 so a total of 45000 + 40500 * 3 = 166500 so total.
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The answer is 18000, method 1: the number from 1 to 9 is 45, the number from 10 to 19 is 55, the number from 90 to 99 is 135, the number from 1 to 99 is 900, the number from 100 to 199 is 1000, and the number from 900 to 999 is 1800, they are in a series of equal differences, so the number from 1 to 999 is 14500 for the number to 1999, The sum of the numbers from 2000 to 2999 is 15500 and so on, with a tolerance of 1000 and a series of 100 terms with 4500, the sum of 10 terms is 166500, so the sum of the numbers from 1 to 9999 is 180000
Method 2: Fill all numbers into four digits, such as 1 to make up 0001, 16 to make up 0016, so it seems to be the arrangement of ten numbers from 0 to 9.
A total of 10,000 numbers, 40,000 numbers, 0-9 each appear 4,000 times 45 times 4,000 times 4,000 = 180,000
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9999 + 1 = 10000 digits sum = 37, excluding zeros.
9990 + 10 = 10000 digits sum = 28, including a zero.
9900 + 100 = 10000 digits sum = 19, including two zeros.
9000 + 1000 = 10000 digits sum = 10, including three zeros.
9009 + 991 = 10000 digits sum = 37 is calculated without zero.
9909 + 91 = 10000 digits = 37 is calculated without zero.
9099 + 901 = 10000 digits = 37 is calculated without zero.
9890 + 110 = 10000 digits = 28, calculated as including a zero.
The sum of 8600 + 1400 digits = 19, calculated as containing two zeros.
This leads to the inclusion of three zeros. There are four groups.
Contains two zeros. There are 45 groups.
Contains a zero. There are 450 groups.
Contains no zeros. There are 4500
Add 5000 as the sum of the middle numbers = 5
Positive integers 1, 2, 3 ......The sum of all numbers of integers, 9998, 9999 is an extended formula: 9*5+(1+2*9)*9*5+9*5*10(1+3*9)+9*5*100(1+4*9)+9*5*1000(1+5*9).
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Make up all numbers into four digits, e.g. 1 makes up 0001 and 16 makes up 0016
In this way, it looks like a ten-digit arrangement of 0-9.
A total of 10,000 numbers, 40,000 numbers, 0-9 appear 4,000 times each.
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There are a total of 9999 single digits, 1 9 each 1000 times, 0 999 times, and the sum of the single digits can be 45000
There are 9999 tens of digits, 1 9 1000 times each, and 0 999 times, and the sum of the tens is 45000
The number of hundreds and thousands is the same as above, and the sum is 45000*4=180000
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Answer: 180000
Explanation: 1+9998=9999 numbers and 9+9+9+9=362+9997=9999 numbers and 9+9+9+9=369998 2 4999 A total of 4999 groups.
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1.Solution: Bringing x=0 into the original equation yields: k crack search + 3k-4 = 0k + 4) (k-1) = 0
k1=-4 k2=1
2.You can use a multiplication formula (perfect square formula or square difference formula) to decompose the factors to get two unary linear equations.
2p)/2]²=2p²-1
p²=2p²-1
The value of 1=p p is p1=1 p2=-23Solution: -x+2 Hunger 6=k x
x²+2√6x-k=0
x²-2√6x+k=0
There is only one rotten source shouting a public point, 0
2√6)²-4k=0
24-4k=0k=6
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1.What is the number that is 50% more than 180?
2.For a project, a certain engineering team worked for 7 days to complete 20% of it, according to this calculation, how many days will it take to complete the project?
28 days. 3.The teacher corrected the essays of the two classes, 30% of the total number was approved in the first lesson, 40% of the total in the second lesson, 24 books in the first lesson, and how many books were approved in the second lesson?
32 copies. 4.There are 24% of the students in the playground kicking the shuttlecock, 36% of the students are playing with the pocket, the students who play the pocket are 6 more than the students who play the shuttlecock, how many students are playing the pocket on the playground now?
18 people. 5.In a brine with a salt content of 20%, how much less salt is than water?
After the price of a product is reduced by 20%, the price is increased by 20%, and the current price is higher than the original price? Or is it lower than the original price?
Therefore, the current price is lower than the original price.
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1 100x(1+50%)=150
5x7 = 35 days.
80x40%-32
6÷12%x36%=16
5 has a water content of 75
Since the content is 20%, let the salt be 20 and the water be 80, so the salt water is 100, and the salt is less than the water (80 20) 80 = 75%.
6 is lower than the original price, which is 96
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It's all a matter of proportions and unary equations, take a good look at the book and do the math yourself......It's not hard.
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1,11 min. 200x12 (200+20)2,190pcs.
3. Truck: 284km passenger car, 568km 852 (1+2) 3 and 1 4 hours 980 square meters.
6x8÷10
The original number is Let the original number be x 10x-x= x=
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1.200 12 (200+20)=minutes) Answer: It takes about 11 minutes to reach the end of the line.
2.A: You can do 190 now.
3.852 3 1 = 284 (km).
852 3 2 = 568 (km).
A: 568 km for buses and 284 km for trucks.
5. s=6×8÷2=24
h=24×2÷10=
6.100x+10y-(10x+y)=10x+y=original number.
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a, b, c are all integers, and a 2 + b 3 = c 4, find the minimum solution of c: a 2 + b 3 = c 4
b^3=c^4-a^2
b 2 * b = (c 2 + a) * (c 2-a) because a, b, c are all integers.
So: c 2 + a = b 2 (1) or c 2 + a = b (3).
c^2-a=b (2) c^2-a= b^2 (4)
1) + (2) or (3) + (4).
Equally: 2c 2 = b 2 + b
Multiply the two sides by 4 to get 1 plus 1 to get
8c^2+1=4b^2+4b +1
Recipe, obtain: 8c 2 + 1 = (2b + 1) 2
Since b is an integer, the minimum value of (2b+1) 2 is 1, i.e., the minimum value of 8c 2+1 is 1
So, 8c 2+1=1
Solution: c=0
c minimum is 0
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I know what you mean, you don't understand in breaking down 2 formulas, right?
Indeed, integers also include negative numbers, so C 2-A and C 2+A cannot tell who is bigger and who is smaller, because A may be ...... negative number
But you can think of it this way, if one of them is negative, then c can't have a minimum, and c can't be infinitely smaller, so c can only be positive, and the same can be carried together, and a and b are also positive.
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