1. Cross the bridge
There are four people going to walk from the left to the right of the bridge tonight. Only two people can walk on this bridge at a time, and there is only one flashlight. You must cross the bridge with a flashlight. The fastest time for four people to cross the bridge is as follows: a 2 points; B 3 points; C 8 points; D 10。 Fast walkers have to wait for slow walkers. 2 1 How to cross the bridge?
Clever insertion of numbers
125 × 4 × 3 = 2000
This formula is obviously not equal, but if two numbers "7" are skillfully inserted into the formula, this equation can be established. Do you know where these two 7s should be inserted?
3. Warm seasons
Spring, summer × autumn and winter = spring, summer, autumn and winter
Spring, summer × autumn and winter = spring, summer, autumn and winter
In the formula, spring, summer, autumn and winter each represent four different numbers. Can you point out what numbers they represent?
4. Broken car going down the mountain
A broken car has to walk two miles, one mile up the hill and one mile down the hill. When it goes uphill, the average speed is 15 miles per hour. How quickly can you reach an average speed of 30 miles per hour on the second mile? Is it 45 miles? You have to think about it!
5. How many eggs does * * * sell?
Mrs. Wang went to the market to sell eggs. The first man bought half the eggs in the basket one after another, and the second man bought the remaining half. At this time, there is an egg left in the basket. How many eggs did Mrs. Wang sell?
6. How many people took the exam?
There are six multiple-choice questions on the test paper, and each question has three options. As a result, the marking teacher found that three answers were randomly selected in all the test papers, and the choice of one question was different from each other. How many people will take the exam at most?
Interesting Mathematical Problems (2)
First, the epitaph of Diophantine.
There is an interesting one-dimensional linear equation problem in the epitaph of Diophantine, an ancient Greek mathematician:
Passerby! Diophantu was buried here, and one-sixth of his life was childhood; After another twelfth of his life, he began to grow a beard; After another seventh of his life, he got married; Five years after marriage, he had a son, but his life expectancy was only half that of his father. After his son died, the old man lived for another four years, ending the rest of his life.
Please calculate the life of Diophantine according to this epitaph.
Second, how to achieve high cost performance?
Forty-five students from the smelly class went for a spring outing in a scenic spot under the leadership of Teacher Shi. When they were ready to buy tickets, they saw a sign that said, "Please buy tickets for tourists: the fare for each ticket is 2 yuan;" Group tickets can be purchased for more than 50 people, and the fare is 20% off. Many students ask, "How can we buy tickets more economically?" "Teacher Shi said," that's a good question. Let's see who can work it out "
Third, divide the apples.
It's autumn, and the apples that the little monkey recruited are all ripe. He chose the best apples, packed them in six boxes, and intended to give them to his good friends Tong Tong and Xinxin. Six boxes were filled with 1 1, 12, 14, 16,17,20 respectively. Because Tong Tong is small and eats little, he intends to give only13 apples to Tong Tong and the rest to Xinxin. These boxes can't be disassembled. Do you know how the tax is divided?
4. Who will win?
In the 3rd Animal Games, the tiger and the lion achieved the same result in the1200m long-distance race. In order to decide the final result, the referee monkey asked the tiger and the lion to play a play-off. The last race of these two beasts is to run back and forth 100 meters, which is the distance of 200 meters. Every step of the tiger is 2 meters, and the lion is 3 meters, but every three steps of the tiger, the lion can only take two steps.
According to the above information, can you judge who will win in advance?
Verb (abbreviation for verb) Number of students
A school numbers each student with 1 at the end and 2 for girls. 1997 1332 1 means "No.32 student in Class 3, Grade 1, 1997 enrolled, male". Then, what year does 1995320 12 mean, what grade and class are they in, and what is their student number?
answer
Interesting math problem (1)
1 Answer: First, A and B cross the bridge together, then B is left on the other side, and A returns alone. When A returns, give the flashlight to C and D and let C and D cross the bridge together. When C and D arrive at the other side, give the flashlight to B and ask B to bring it back. Finally, A and B cross the bridge together again. Then the required time is: 3+2+ 10+3+3=2 1 min.
Answer to question 2: The formula after inserting numbers is: 1725×4×3=20700.
The answer to question 3: Spring = 2; summer = 1； Autumn = 8; Winter =7
Answer to question 4: The average speed of a broken car can't reach 30 mph in any case. Because when the average speed is 30 miles per hour, the total time for the broken car to go up and down the mountain should be115 hours. It took115 hours to climb the mountain. So the average speed of broken cars is less than 30 miles per hour.
Answer to question 5: Mrs. Wang sold 10 eggs.
Answer to question 6: At most 13 people take the exam. I'm not sure about the specific thinking process. Please give us your advice!
Interesting Mathematical Problems (2)
1. Let Diophantine's life span be x years.
x/6+x/ 12+x/7+5+x/2+4=x
Simplify this equation to get 75x/84+9 = x.
X=84 is obtained by solving.
In other words, Diophantine's life span is 84 years.
2. Amount payable for purchasing 46 individual tickets: 2×46=92 yuan.
Amount payable for purchasing 50 group tickets: 2×50×80%=80 yuan.
Buying group tickets is less than buying individual tickets: 92-80= 12 (yuan).
That is, buying group tickets is less than buying individual tickets. 12 yuan, you should buy group tickets.
Three or six boxes * * contain apples11+12+14+16+17+20 = 90 (pieces), so Tong Tong should divide apples by 90 ×/. Because 14+ 16=30 (pieces), two boxes of apples with 14 and 16 should be given to Tong Tong and the rest to Xinxin.
Fourth, the tiger runs 2×3=6 (meters) in three steps; The lion took two steps and ran 3×2=6 (meters). So tigers and lions run at the same speed. But the tiger just ran 50 paces 100 meters, and the lion has to take another step after running 99 meters, reaching 102 meters, and then running back. In this way, the lion ran 4 meters more than the tiger, so the tiger won.
The verb (the abbreviation of verb) 1995320 12 indicates that the student is in Class 2, Grade 3 and is studying at 1995. The student's student number is 1, and she is a girl.
Correct alarm clock
Answer: I always spend 4 hours and 50 minutes (7: 00- 1 1: 50). Apart from playing time, I have to walk for 3 hours and 20 minutes. Because the walking time is equal, it is 1 hour 40 minutes, and the exact time to leave the museum and start walking home should be 8: 50+ 1: 30 = 10: 20, so the time to go home should be10: 20+1:40. At this time, it is accurate to set the alarm clock to 12.
Why is 1 yuan missing?
Answer: Apple is RMB per kilogram 1 yuan, pear is RMB per kilogram, and after mixing, RMB per kilogram (1+ )÷2= RMB, while Xiaoming only accepts 2 yuan for 2.5 kilograms, that is, RMB per kilogram. This charges-= yuan per kilogram. Apples and pears cost 1 yuan at 30kg.