A pair of lovers meet in the lotus pond from 8 to 9. The first one waits for 25 minutes and then goes by himself. Assuming that everyone has the same probability of reaching the lotus pond at any time between 8: 00 and 9: 00, what is the probability that the lovers can't meet?
3. Can you put the numbers 0, 1, …, 9 on the circumference so that the difference between any two adjacent numbers is 3, 4 or 5?
4. At 12 hour, when the hour hand and the minute hand on the clock face just form an angle of 60 degrees. For example, at 2 o'clock, the hour hand and the minute hand make an angle of 60 degrees. Please write down at least five situations and give reasons.
5. Two people take turns to take numbers from the nine numbers 1, 2, …, 9. One at a time, whoever takes three numbers first, if the sum of the three numbers is 15, who is the winner. If the number of 1 is 5, what number should the second person take to make himself invincible?
6. There is a "2 1 point" game in poker. The starting rules are as follows: take four paper cards at will (except Big and Xiao Wang), and add, subtract, multiply and divide these four numbers to make the result equal to 24 (A= 1, J = 1, Q = 65438). For example, for the four cards 1, 2, 3 and 4, we can calculate as follows:
( 1+2+3)×4=24.
If you add, subtract, multiply and divide the four cards A, 2, 3 and 4, you can get the following results:
(2- 1)×(4-3)= 1; (2+ 1)-(4-3)=2;
(2+ 1)×(4-3)=3; (2+ 1)+(4-3)=4; ……
So ask: How much can the above operations make the calculation results continuously calculated?
Changing four cards can make the calculation results more continuous? For example.
What if the operation is not limited to four operations, but can be multiplied and squared?
7.a, B, C, D, E, F and G are arguing about "What day is it today?"
The day after tomorrow is Wednesday. No, today is Wednesday.
C: You are all wrong. Tomorrow is Wednesday. D: nonsense! Today is neither Monday nor Tuesday nor Wednesday.
I'm sure yesterday was Thursday. F: No, you have it backwards. Tomorrow is Thursday.
G: Anyway, yesterday was not Saturday.
In fact, only one out of seven people is right.
Excuse me: Who is right? What day is it today? Please provide a justification for the answer.
8. A cube with 1, 2, 3, 4, 5, 6 written on six sides is called a dice.
Q: (1)*** How many different kinds of dice are there?
(2) The absolute value of the difference between numbers on two adjacent faces is called the variation between these two faces, and the sum of the variations is called the total variation (represented by V). In all the dice, find the maximum and minimum value of v.
9. if a=b and a, b > 0, test a=2a.
10. One of the most common matching games is that two people play together. First, put some matches on the table, and two people take turns taking them. If a takes them first. You can first limit the number of matches taken at a time and stipulate that the person who takes the last match wins.
Rule 1: If the number of matches taken at a time is limited to at least one and at most three, how can you win by playing armor?
Rule 2: Limit the number of matches taken at one time, not continuous numbers, but some discontinuous numbers, such as 1, 3, 7. How can I win by playing A?
25 cases of mathematical problems in life ※ Big-headed son and small-headed father * * * opened a McDonald's shop together. They calculated the turnover of one day together in the evening and found that there was 32. 13 yuan on the books. Later, I found that the decimal point of a sum of money was wrong. It turned out that the money was ().
Teacher Wang bought 72 pens for the students, and spent □67.9△ yuan, of which I can't remember the math except □ and △. Please help the teacher with his math. How much is each pen? ※?
Smile and finish a bottle of juice four times. Drink one sixth of a bottle of juice for the first time, and then fill it with water. ※: The second time I drank a third bottle, then filled it with water, and the third time I drank half a bottle and filled it with water; Gulp it off for the fourth time. Drink less juice and drink less water.
A primary school numbers each student, with the numbers of boys ending in 1 and girls ending in 2. For example, 964 10252 means "I entered school in 1996, and my classmates are girls. ※. Then 0111kloc-0/01indicates that the student is a () student in Class () of Grade (), and his student number is (). If you are in Class 36, Grade 6, please fill in your student number in the above way.
There are two ways to pay for PHS mobile phones in a certain area: (1) free of monthly fee. 0.25 yuan per minute, basic monthly consumption 15 yuan. ※: (2) Pay the monthly fee of 18 yuan per month, and the call is 0. 1 yuan per minute. Please calculate the monthly call time as 100 minutes, 200 minutes. Which way is more cost-effective? If your father also has a PHS, which way do you think is better for him to pay? Why?
The tap water charge in a city is as follows: the monthly water consumption of each household15t (including15t) is charged according to one ton of 0.9 yuan; If it exceeds 15 ton, it will be charged as one ton in 3 yuan. A family used 2 1 ton of water in April. ※. How much should it pay for water?
Once, three friends, A, B and C, took a taxi to go out on business. When they set out, they agreed to share the fare reasonably. Get off at 6 km early, 12 km, 18 km, pay the fare to 36 yuan. ※. How much fare do the three of them have to bear?
A peasant woman is carrying a basket of eggs to sell. The first time she sold half and more eggs, the second time she sold the remaining half and more, the third time she sold the remaining half and more, and finally there was an egg left in the basket. How many eggs does that peasant woman have? ※?
There are five boxes of biscuits in a food store. If you take out 15 kg from each box, the remaining five boxes of biscuits are exactly the original two boxes. How many kilograms of biscuits are there in each box? ※?
Xiao Liang and his father went for an outing by taxi. 5 yuan will be charged within 10 km, and 0.3 yuan will be charged every km beyond 10 km. When they get off the bus, Xiao Liang will pay 9.2 yuan's taxi fare. How many kilometers did they walk by taxi? ※?
Fifty-two students from Class Six (1) went to the aquarium. At noon, the teacher asked Beibei to buy drinks for everyone. Because I bought a lot, my aunt gave me a discount to buy one box and get one free. ※. * * * paid four boxes, one for each person. Do you know how many boxes there are in each box of drinks?
A primary school wants to buy 60 footballs, and now there are three stores A, B and C to choose from. The football prices of the three stores are all within 25 yuan, but the preferential measures of each store are different. ※:
Shop A: Buy 10 football and get 2 free; If you buy less than 10, you won't get them.
Shop B: 5 yuan is quoted for each football;
Shop C: After shopping in 200 yuan, I will return to 30 yuan.