※ Mr. Wang bought 72 pens for the students, *** with □ 67.9 △ yuan, of which □ and △ outside the math has not remembered the table, please help the teacher to calculate. How much is each pen?
*Smiley drinks a bottle of juice in four sips. The first time he drank one-sixth of a bottle of juice and then filled it with water; the second time he drank one-third of a bottle and then filled it with water; the third time he drank half of a bottle and then filled it with water; and the fourth time he drank it all in one go. The juice Xiaoxiao drank was ( ) and the water he drank was ( ).
※A elementary school for each student number, set the number of untailed 1 means boys, for 2 means girls. For example, 96410252 means "enrolled in 96, in the fourth grade class, 025 students, the student is a girl". Then, 01110101 means that the student is a ( ) student enrolled in ( ) year, in ( ) grade ( ) class, school number is ( ). If you are student number 36 in class 3 of grade 6, please use the above method to make up your school number.
※There are two ways to pay for SmarTone cell phones in a certain area: (1) No monthly fee. Calls cost 0.25 yuan per minute, and the basic monthly consumption is 15 yuan; (2) pay the monthly fee, which is 18 yuan per month, and calls cost 0.1 yuan per minute. Please do the math. 100 minutes and 200 minutes of calls per month, which is the more cost-effective choice? If your father also has a SmarTone, do you think it is better for him to pay the fee in that way? Why?
*The water tariffs of a certain city are stipulated as follows: 15 tons of water (including 15 tons) per household per month is charged at 0.9 yuan per ton, and the excess over 15 tons is charged at 3 yuan per ton. A household in April, 21 tons of water, how many yuan should pay the water bill?
※ once, a, b, c three friends to share a cab to go out to do business, set off three people discussed, the fare by three reasonable share. Early in the line to the 6 km place to get off, B in the line to the 12 km place to get off, C has been traveling to the 18 km place to get off, and paid 36 yuan of the fare, ask them how much each should bear the fare is more reasonable?
※ a farmer's wife with a blue eggs to sell, the first sold half of all the eggs and more than half, the second sold the rest of the half and more than half, the third sold the rest of the half and more than half, the last basket is still left in an egg, ask: the farmer's wife originally have how many eggs?
※A food store has 5 boxes of cookies, if you take out 15 kilograms from each box, then the remaining cookies in the 5 boxes is exactly the original two boxes of cookies, how many kilograms of cookies were in each box?
*Small bright and his father to take a cab to the countryside, 10 kilometers within the charge of 5 yuan, more than 10 kilometers, the charge per kilometer of 0.3 yuan, get off the small bright *** to pay the cab fare of 9.2 yuan, how many kilometers the cab line?
※Six (1) class 52 students went to the Oceanarium tour, the teacher let Beibei buy drinks for everyone at noon. Because of the buy more, the aunt gave to buy a box to get a box of discount, **** paid 4 boxes of money, exactly one box per person. Do you know how many boxes there are in each case?
※ A elementary school to buy 60 soccer balls, now there are A, B, C three stores to choose from, three stores soccer ball price is 25 yuan, but each store's preferential approach is different:
Store A: buy 10 soccer balls free of charge, 2, less than 10 will not be given away;
Store B: each soccer ball discount of 5 yuan;
Store C: shopping for every full 200 yuan, cash back 30 yuan;
Store C: shopping for every full 200 yuan, cash back 30 yuan.
In order to save money, which store should Hope Elementary School buy from and why?
※ blasters to blast an old bridge, according to the blasting situation, the safety distance is 70 meters (personnel should be withdrawn to 70 meters away), the following are some known data, the speed of the personnel is 7 m / s, the burning speed of the fuse is 10.3 cm / s. How long should the fuse be in order to ensure the safety of this blasting?
*A middle school library purchased three hardcover and five paperback copies of the Chinese Dictionary,*** using 27.8 yuan. If you use a hardcover to exchange two paperbacks still have to pay another 1 yuan, how many yuan per hardcover dictionary?
※Sixth grade there are three classes A, B, C, known A, B class *** have 50 people, B, C class *** have 70 people, A, C class *** have 60 people, ask how many people in each of the three classes A, B, C?
*Wang bought a coat, a hat and a pair of shoes for 140 yuan. The price of the coat is 90 yuan more expensive than the hat, and the coat and hat are 120 yuan more expensive than the shoes, how much is the price of a pair of shoes?
*Three ****, A, B, and C, paid $27 for a batch of exercise books, each paying $9. Since B and C took 15 more books than A, B and C each had to give A 1.5 yuan, how many exercise books did the three buy?
※ an elementary school organized 325 teachers and students to go on a spring trip, known as the bus is limited to 40 people, 1000 yuan per day each, the minibus is limited to 25 people, 650 yuan per day each, ask how to rent a car is appropriate?
※There are two job advertisements, A company's salary using the annual salary system, the starting salary of 10,000 yuan per year, and then increased year by year, an increase of 600 yuan per year; and company B semi-annual salary system, the starting salary of 5,000 yuan every six months, and then increased by 200 yuan every six months, ask the company's conditions are more favorable?
※ A, B two people to explore the desert, they go 20 kilometers a day to the depth of the desert, known that each person can carry a maximum of one person 24 days of food and water, if not allowed to store some of the food on the way, ask: one of them can be as far as how many kilometers deep into the desert? If it is possible to store some of the food on the way back for use on the way back, how far into the desert can one of them go?
*Small Qiang, Xiaowei and Xiaohua help Grandma Li to bring two suitcases of the same weight to the station 1.5 kilometers away from each other. The three of them decide to bear the burden of running Li's task evenly, and each of them can only carry one suitcase at a time, so how many kilometers can each of them carry on average?
※ A, B, C three 60-meter race, when A crossed the finish line, 10 meters ahead of B, 20 meters ahead of C, if the speed of each remains unchanged, ask when B crossed the finish line, how many meters ahead of C?
※ Auntie Li took 120 yuan to the market to buy meat, because the price of meat is reduced by one-fifth, so she bought more meat than last time with the same amount of money to buy 5 kilograms, ask: the original price of meat is how many yuan per kilogram?
※Movie tickets were originally priced at a number of yuan, and now the price has been reduced by 3 yuan each. The audience has increased by half, and the revenue has also increased by one-fifth.
1. Someone wrote a program, starting from 1, alternately do multiplication or addition, (the first time can be addition, can also be multiplication), each addition, the last operation will be added to the results of the 2 or 3; each multiplication, the last operation will be multiplied by 2 or multiply the results of the 3, for example, 30, it can be obtained in this way: 1 +3 = 4 * 2 = 8 +2 = 10 * 3 = 30, how can I get: 2 How can I get: 2 of 100 times + 2 of 97 times - 2
Answer: 1 + 3 = 4 + 2 = 2 of 3 times - 2 = 2 of 3 times + 2 - 2 = (2 of 3 times + 2 - 2) * 2 = ...... = = 2 of 100 times + 2 of 97 times - 2 of 97 times = 2 of 100 times + 2 of 97 times - 2 of 97 times + 2 = 2 of 100 times + 2 of 97 times - 2 of 97 times + 2 = 2 of 100th + 2's 97th - 2's 97th + 2+2=......=2's 100th + 2's 97th - 2
2. The following poem is out of the writings of Xu Ziyun, a mathematician of the Qing Dynasty. How many monks are there in the poem?
The lofty ancient temple is in the clouds, I don't know how many monks are in the temple.
Three hundred and sixty-four bowls, let's see if they are used up and not poorly contested.
Three people **** eat a bowl, four people **** eat a bowl of soup.
Please ask Mr. Ming calculator, calculate how many monks in the temple?
Answer: three people **** eat a bowl: one person with one-third of the bowl when eating,
four people **** eat a bowl of soup: one person with one-quarter of the bowl when eating soup,
two total, then each person with 1/3 + 1/4 = 7/12 bowls,
Set **** there are monks X people, according to the meaning of the question:
7/12X = 364
The solution gives, X=624
3. Two boys, each riding a bicycle, start riding in a straight line toward each other from two places 2O miles (1 mile is 1.6093 km) apart. At the moment they start, a fly on the handlebars of one bicycle begins to fly straight toward the other. As soon as it reaches the handlebars of the other bicycle, it turns and flies back. The fly goes back and forth, between the handlebars of the two bicycles, until the two bicycles meet. If each bicycle is traveling at an equal speed of 1O miles per hour, and the fly is flying at an equal speed of 15 miles per hour, how many miles did the fly fly fly in total***?
Answer: each bicycle is moving at 10 miles per hour, and the two will meet at the midpoint of a 2O-mile distance in 1 hour. The fly is traveling at 15 miles per hour, so in 1 hour it has traveled a total of **** 15 miles.
4. "Sun Tzu Calculating Scriptures" is one of the famous "Ten Books of Calculating Scriptures" which was used as a textbook of "arithmetic" in the early Tang Dynasty, *** three volumes, the first volume describes the system of counting chips and multiplication and division laws, the middle volume gives examples of the method of counting fractions and the method of opening and leveling, all of which is an important source of information to understand the ancient Chinese arithmetic. The next volume collects some arithmetic puzzles, and the problem of "chicken and rabbit in the same cage" is one of them. The original question is as follows: There is a cage of pheasants (chickens) and rabbits, with thirty-five heads on the top and ninety-four feet on the bottom. What is the geometry of the male and the rabbit?
Solution: Let x be the number of pheasants and y be the number of rabbits, then we have
x + y = b, 2x + 4y = a
The solution is: y = b/2-a,
x = a-(b/2-a)
According to the set of formulas, the answer to the original question can be easily obtained. easy to arrive at the answer to the original question: 12 rabbits and 22 pheasants.
5. Let's all try to run a hotel with 80 suites and see how knowledge can be transformed into wealth.
A survey showed that if we set the daily rent at $160, we would have a full house; and for every $20 increase in rent, we would lose three guests. The daily expenses for service, maintenance, etc., for each occupied room **** amount to $40.
QUESTION: How should we price our rooms to make the most money?
Answer: $360 per day.
While it is $200 higher than the full price, so we lose 30 guests, the remaining 50 guests will still bring us 360*50=18,000 yuan; after deducting the expenses of 50 rooms 40*50=2,000 yuan, the daily net profit is 16,000 yuan. And the net profit is only 160*80-40*80=9600 yuan when the guests are full.
6. Mathematician Wiener's age: the cube of my age this year is a four-digit number, and the fourth power of my age is a six-digit number, and these two numbers, which just happen to be the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, are all used, and what is Wiener's age?
Solution: Wiener's age is x, first of all, the cube of the number of years is a four-digit number, which determines a range. 10 of the cube is 1000, 20 of the cube is 8000, 21 of the cube is 9261, is a four-digit number; 22 of the cube is 10648; so 10 = <x< = 21 x quadratic is a six-digit number, the quadratic of 10 is 10,000, the cube is not far from the six-digit number, but it is a six-digit number. The fourth power of 10 is 10,000, which is not even close to a six-digit number. 15 is 50625, which is not a six-digit number. 17 is 83521, which is not a six-digit number. 18 is 104976, which is a six-digit number. 20 is 160,000, and 21 is 194,481, which is 18 = <x< = 21, which is one of the four numbers 18, 19, 20 and 21. One of the four numbers; because these two numbers just put the ten numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 all used, four-digit and six-digit just use the ten numbers, so there is no duplication of digits in the four-digit and six-digit numbers, now come one by one to verify that, 20 of the cubic is 80,000, there is a duplication; 21 of the quadruple is 194481, there is also a duplication; 19 of the quadruple is 130321; also repeated; the cube of 18 is 5832, and the quadratic of 18 is 104976, neither of which is repeated. Therefore, Wiener's age should be 18.
7. Put 1,2,3,4......1986,1987 the 1987 natural numbers evenly lined up in a large circle, counting from 1: cross 2,3 across 1; cross 5,6 across 4, so that every other number crosses off two numbers, and turn around and cross it down, asking: finally Which number is left.
Answer: 663
8. In a 90-cm-long, 40-cm-wide painting of a landscape around the perimeter of the up a width of the same golden paper edge, made of a wall map, if the area of the landscape is required to be the entire area of the wall map of 72 percent, then the width of the golden paper edge should be how much?
Answer: According to the question, there are (90+2X)(40+2X)*72%=90*40
(90+2X)(40+2X)=3600/0.72
3600+180X+80X+4X2=5000
4X2+260X-1400=0
( 4X-20)(X+70)=0
Get 4x-20=0 X+70=0
4*x=20 X=5
X=-70 does not hold
So X=5cm
9. A soccer ball sewn from black and white color leather blocks, black leather blocks are square pentagon and white leather blocks are square hexagon, if a If there are 32 black and white leather blocks on the ball, calculate the number of black and white leather blocks
Answer: Equivalence:
Number of edges used in the white leather blocks *** with the black leather blocks = number of edges used in the black leather blocks *** with the white leather blocks
Let there be a white block of leather x
3x=5(32-x)
Solve for x =20
10. There are ten identical black socks and ten identical white socks in the drawer. If you open the drawer in the dark and reach for the socks, how many socks must you take out at least to be sure that you have got a pair?
Answer: 3
11. Four people, Xiao Zhao, Xiao Qian, Xiao Sun and Xiao Li, are discussing which team will win the final of a soccer match. Xiao Zhao says, "D pair is bound to lose, while C team can win." Qian says, "Team A, Team C will win and Team B will lose at the same time." Sun Jr. says, "Team A, B team C can win." Li said, "Team A losing, team C, team D winning is obvious."
They have already said which team wins in their words, can you guess correctly which team actually wins the championship?
Answer: Four people, Zhao, Qian, Sun and Li, are discussing which team will win the final of a soccer match. Zhao says, "D pair will lose, while C team can win." Qian says, "Team A, Team C will win and Team B will lose at the same time." Sun Jr. says, "Team A, B and C can win." Li Jr. said, "Team A losing and Team C, Team D winning is a clear scenario."
Chiu's words mean that team D loses
Chin's words mean that team B loses
Sun's words mean that team D loses
Lee's words mean that team A loses
So, team C wins
12. If three line segments of lengths a, b, and c can form a triangle, can the line segments root number a, root number b, and root number c form a triangle?
If yes or no, prove it
If no, give an example.
Solution: it can.
It may be assumed that a is the smallest and c is the largest, then the sufficient condition for abc to form a triangle is a+b>c;
Then √a+√b is compared with √c, which is actually a+b+2√ab compared with c (squared on both sides), and a+b is already greater than c. Then obviously a triangle can be formed.
13. A farmer met the devil, who said, "I have an idea that will make you rich! As long as you walk across this bridge from behind me, your money will be doubled, walk back and doubled again, every time you cross the bridge, your money can be doubled, but you must guarantee that each time after you double the number of money to give me a steel plate, the farmer was delighted, immediately cross the bridge, three times after crossing the bridge, the pocket just only a steel plate, pay the devil, not a penny, please have a monomial containing a to indicate that the farmer initially pockets the Please have a monomial containing a to represent the number of steel plates in the farmer's pocket initially.
Answer:Let the initial amount of money be x
2[2(2x-a)-a]-a=0
Solve the equation to get x=7a/8
14. Three students going home from school, on the way to see a yellow car, and then when they went further, they heard that the car hit an old man and fled. But no one wrote down the license plate number of the car. When the police questioned the three high school students, they all said the license plate number was a four-digit number. One of them remembers that the first two digits of the number are the same, another remembers that the last two digits of the number are the same, and the third remembers that the four-digit number happens to be a perfect square. Can you determine the license plate number of the car that was involved in the accident
Answer: The four-digit number can be expressed as
a × 1000 + a × 100 + b × 10 + b
=a × 1100 + b × 11
=a × 1100 + b × 11 11
=11×(a×100+b)
Because a×100+b must be divisible by 11, a+b = 11, which carries over into the above equation to get
Quadruple digit = 11×(a×100+(11-a))
=11×(a×99+11)
=11 × 11 × (9a + 1)
As long as 9a + 1 is a perfect square.
Verified by a = 2, 3, 4, 5, 6, 7, 8, 9, 9a + 1 = 19, 28, 27, 46, 55, 64, 73.
So there's only one solution for a = 7; b = 4.
So the four-digit number is 7744 = 11^2 x 8^2 = 88 x 88
15.It is known that 1 plus 3 is equal to 4 is equal to 2 of 2, 1 plus 3 plus 5 equals 9 equals 3 of 2, 1 plus 3 plus 5 plus 7 = 16 equals 4 of 2, 1 plus 3 plus 5 plus 7 plus 9 equals 25 equals 5 of 2, etc. ......
<1> Following the example above, calculate 1 plus 2 plus 3 plus 5 plus 7 plus... Plus 99 equals?
<2> Based on the above pattern, express the general pattern in terms of the natural number n (n is greater than or equal to 1).
Solution: <1>1+3+5+... +99=50 squared
<2>1+3+5+... +n=[(n-1)/2+1] squared
16.Once a cat caught 20 mice and lined them up. The cat announced its decision: first, it would eat the mice standing in odd places, then it would renumber the remaining teachers by 1, 2, 3, 4... and then eat all the mice standing in odd places. This is repeated so that the last remaining mouse will be released. A smart mouse listens and immediately picks a spot, and it is indeed the last one left, and the cat sets it free!
Do you know what position the clever little mouse stood in?
Answer: 16th in line. The 1st one that can be divided by 2 is left, the 2nd one that can be divided by 4(2 squared) is left, the 3rd one that can be divided by 8(3 times 2) is left, and the 4th one that can be divided by 16(4 times 2) is left, so only the 16th one will not be eaten.
17.1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+...+1/(98*99*100)
Solution: 1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+...+1/(98*99* 100)
=(1-1/2-1/3)+(1/2-1/3-1/4)+(1/3-1/4-1/5)+..... .1/98-1/99-1/100
=1-1/100
=99/100
Remarks: 1/(1*2*3)=1-1/2-1/3
18.Xiaowei and Xiaoming exchanged information about their activities in the summer vacation, and Xiaowei said, "I participated in the science and technology camp and went out for a week, the sum of the number of dates of these seven days is 84, do you know what date I left?" Xiaoming said, "I went to my uncle's house for seven days during my vacation, and the sum of the number of dates plus the number of months is also 84, can you guess what day of the month I came home?
Answer: First question: Let the day of departure be the Xth
X+X+1+X+2+X+3+X+4+X+5+X+6=84
X=9
Smallway left on the 9th.
Second question: Since it is a summer vacation activity, it can only be in July or August
Set the day of return to be the Xth
Listed as
7+X+X-1+X-2+X-3+X-4+X-5+X-6=84
Or
8+X+X-1+X-2+X-3+X-4+ X-5+X-6=84
The first equation solves X=14
The second equation result is not integer
So it can only be July 14th to arrive at home
19.There are three classes in the first year of a school, A, B and C. There are 4 more girls in class A than in class B. There is one more girl in class B than in class C. If the first group of students in class A is transferred to class B, and at the same time the If the first group of students from class A is transferred to class B, while the first group of students from class B is transferred to class C, and the first group of students from class C is transferred to class A, then the number of girls in the three classes is exactly equal. Knowing that there are 2 girls in the first group of class C, how many girls are there in the first group of each of classes A and B?
Answer: Let there be m and n girls in the first group of classes A and B respectively. There are x girls in class C. There will be x+1 in class B. There will be x+5 in class A. The average is x+2 (using change of quantities to compute) Class C: -2+n=(x+2)-x
Class A: +2-m=(x+2)-(x+5) It can be concluded that m=5 n=4
20. there are A reservoir, which has a certain amount of water flow per unit of time, also releases water to the outside. The water in the reservoir can be used for 40 days at the present rate of release. Due to recent rainfall in the reservoir area, the amount of water flowing into the reservoir has increased by 20%, and if the amount of water released also increases by 10%, then it can still be used for 40 days. Q: How many days can the water be used if it is released at the original release rate?
Answer: Let the total volume of water in the reservoir be x. The inflow and outflow of water in a day will be m and n, respectively
Then we have x/(n-m)=40=x/[n(1+10%)-m(1+20%)] Requirement x/[n-m(1+20%)]
You can simplify the first to get n=2m x=40m and bring it into the second equation to get x=50 days < /p>
21. a hotel first A and B two kinds of air-conditioning temperature is set to 1 degrees, the results of A air-conditioning than B air-conditioning daily more than 27 degrees of power savings and then B air-conditioning cleaning equipment, so that B air-conditioning every day, the total amount of power savings is only 1 degree higher temperature after the amount of savings of 1.1 times and A air-conditioning savings remain unchanged so that the two kinds of air-conditioning per day **** savings of 405 degrees of power to ask for the temperature only 1 degree higher temperature bar How many kilowatt-hours per day *** are saved by raising the temperature bar by only 1 degree?
Solution: After raising the temperature by only 1 degree, each of the two air conditioners A and B saves X and Y degrees of electricity per day
X-Y=27,
X+1.1Y=405
X=207
Y=180
The two air conditioners A and B each saves 207,180 degrees of electricity per day.
22. Cotton Tree Village has 1,000 hectares of barren mountains, the greening rate of 80%, 300 hectares of good land does not need to be green, X hectares of river slopes this year, planting trees and greening rate of 20%, so that all the land of Cotton Tree Village, the greening rate of 60% of the river slopes*** How many hectares of river slopes?
Solution: (x*20%+1000*80%)/(1000+300+x)=60%
(0.2*x+800)/(1300+x)=0.6
0.2*x+800=780+0.6*x
x=50 hectares
23. A sheet of paper is 0.06 cm thick. 0.06 cm,the distance from the earth to the moon is 3.85*10^5 km.
Small Ming says that if you cut the paper into two equal parts, stack the paper cut into two equal parts, and cut it into two equal parts again, if you repeat this, the height of all the paper is greater than the distance from the moon to the earth.
Gang said, "I don't believe what Ming said.
Is Ming's story right? Why?
Answer: 40 cuts would be higher than 3.85*10^5 kilometers
2^40*0.06/100000=6.597*10^5 kilometers
Xiaoming's statement is right, except that the piece of paper must be big enough, or it can't be cut after a few cuts
24. There are 27 pearls, and one of them is a fake one, but the appearance is the same as the real pearls, only a little lighter than the real pearls. Q: At least with the balance weighing a few times (without weights), you can certainly find out the fake pearl?
Answer: 3 times
The first time the 27 pearls into three equal parts, take two of them on both ends of the balance weighing, if the balance is skewed, then consider the light of the nine pearls, if not skewed, then consider the nine did not weigh; similarly, the nine pearls and then divided into three equal parts, taking two of them put on the balance at both ends of the weighing, and then again to get the three "suspicious" pearls, take out two weighing, if the balance is skewed, then take out the nine pearls, take out the nine pearls, take out the nine pearls. two weighing, if the balance is skewed, the light is inferior ~ otherwise did not weigh is inferior
25. Egypt, like China, is also the world's famous ancient civilizations, the ancient Egyptians dealt with fractions is different, they generally only use the molecule for the fraction of 1, for example, with 1/3 +1/15 that 2/5, with 1/4 +1/7 +1/28 to indicate 3/7 and so on, and now with the 90 Egyptian numerators 1/2, 1/3, 1/4, 1/5, ...... . 1/90. 1/91, are there 10 more of these numbers, with plus and minus signs so that they sum to -1. If there are, write the 10 numbers, if not, give reasons.
Solution:I Solution:
-1=-1/5-1/6-1/8-1/9-1/10-1 /12-1/15-1/18-1/20-1/24
Solution 2:
1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6- 1/7+1/7-1/8+1/8-1/9+1/9-1/10=1-1/10
So:
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/10=1
That is:
-1/2-1/6-1/12 -1/20-1/30-1/42-1/56-1/72-1/90-1/10=-1
24. There were three people who went to a restaurant and each of them took out 10 pounds and each of them took out 30 pounds. The three of them took 30 pounds and paid the owner for the meal. The owner got back 5 pounds and asked the waiter to give it back to them. The waiter then thought: How can I give 5 pounds to three people? The waiter thought, "How can I divide ￡5 among three people?" So he took a ￡2 tip for himself, and gave the remaining ￡3 to each of the three people, so that's ￡9 each for the meal, and ￡27 for the three people, but with the two pounds taken by the waiter, it's ￡29, so where's the rest of the ￡1 going?
25. n playing cards numbered 1, 2, 3 ......n are stacked in order. The top card (numbered 1) is dealt out, the next card (numbered 2) is placed at the bottom of the stack, the next card (numbered 3) is dealt out, and so on until all cards have been dealt. Please answer the following questions:
(1) What is the last card? In particular, what are your results when n=13, 54, 1000 respectively?
(2) If the cards dealt out happen to be in such an order as 1, 2, 3, ......n, ask how the original cards were arranged. It is required to give the algorithm and the corresponding implementation program. The other, when n = 13, 54, how exactly are the cards arranged?
26. Li Bai, the great poet of the Tang Dynasty, often drank wine and composed poems.
Li Bai walks on the street, carrying a jug to buy wine.
When he meets a store, he doubles the price, and drinks a bucket of wine when he sees a flower.
Three times he met a store and a flower, and drank all the wine in the pot.
Please guess, there is wine in the pot
Please ask why the formula is like this: 1 divided by 2 plus 1, then divided by 2 plus 1, then divided by 2 equals to 7/8 of a bucket
26. There are 4 numbers 5,5,5,1, and the final result of adding, subtracting, multiplying and dividing them alone is 24, but note that squaring, cubing and multiplying can not be used.
27.
Modern society, the rabbit family in order to save the face of the ancestral race failure, decided to race again with the turtle family. In the war book the hare family, in order to show their strength, said that first let the turtle run 500 meters (the whole 2000 meters).
The tortoise family got the letter of war, held a meeting of the whole family to discuss countermeasures. According to the strength of the turtle is impossible to win, but do not want to lose face of their ancestors. Just then, a divine turtle appears, claiming to outsmart his opponent.
Finally the Turtle family replies: Physical fitness is important in modern society, but intelligence is more important. We can beat you on the tabletop, so why bother with a race, if you have the guts to meet us on the tabletop!
The rabbit family thought that strength determines everything and was not afraid to go on the table, so they gladly agreed!
Before the tabletop, the divine turtle said: Because of your arrogance, you have lost the chance to save the face of your ancestors. Here is my argument
Set the speed of the turtle as v1, the speed of the rabbit as v2, because the rabbit first run 500 meters, so set the turtle and the rabbit are separated by s0, as shown in the figure,
a b c d
|---------s0---------|-------s1--------|------s2--------|- The rabbit needs time t1 to get to a, and the turtle runs to b in t1 time; the rabbit needs time t2 to get to b, and walks to c in t2 time; the rabbit needs time t3 to get to c, and the turtle runs to d in t3 time, and so on, so that the rabbit can only be infinitely close to the turtle, but can't catch up with the turtle, so the rabbit can't win the turtle.
The rabbit family thought for a long time and did not find any problem with the turtle's reasoning. Regretting that they let the tortoise run 500 meters first, they regretted it too late and could only admit defeat and go home.
But let's think seriously, in reality the rabbit can catch up with the turtle, but why? What was wrong with the turtle's reasoning?
27. The fruit store has 60 apples of both sizes, the big apples are sold at two per dollar, and the small apples are sold at three per dollar.
It can be known that the big apples are sold at 60/2 = 30 yuan, and the small apples are sold at 60/3 = 20 yuan.
The new salesman accidentally mixes the two kinds of apples and ****s up 120 apples. He thought it would be better to sell them at 5 apples per two dollars. But after he sold them, he got 120/5*2 = 48 dollars. But it should have been 50 dollars. Q, where did the two dollars go?
28A, B, C, D, four students to participate in table tennis singles tournament, before the game, four students on the outcome of the game said:
A: "I will get first place" B: "A, C will not get first place"
C: "A or B will come in first place" D: "B will come in first place"
Two students turned out to be right. Q: Who will win this final playing first place?