One end of incense point A, two ends of incense point B. By the time incense B burned out, it was already 30 minutes. Then ignite the other end of incense A, and the time from this time to burning A is 15 minutes.
A manager has three daughters. The ages of the three daughters add up to 13, and the ages of the three daughters add up to the manager's own age. A subordinate knows the manager's age, but still can't determine the age of the manager's three daughters. At this time, the manager said that only one daughter's hair was black, and then the subordinates knew the age of the manager's three daughters. What are the ages of the three daughters? Why?
The three girls should be 2 years old, 2 years old and 9 years old. Because only one child has black hair, that is, only she has grown up, and the other two are still very young, that is, less than 3 years old, with light hair. The reorganization manager should be at least 25 years old.
Three people went to a hotel and stayed in three rooms. Each room cost $65,438+00, so they paid the boss $30. The next day, the boss thought that $25 was only enough for three rooms, so he asked my brother to return $5 to three guests. I didn't expect my brother to be greedy. He only paid back 1 dollar and secretly took 2 dollars himself. But at the beginning, the three of them paid 30 dollars, so 1 dollar?
Typical concept of stealing. In fact, three people only went out of 27 yuan, the eldest got 25 yuan and the younger got 2 yuan.
There are two blind people. They all bought two pairs of black socks and two pairs of white socks. Eight pairs of socks are of the same material and size, and each pair of socks is connected with trademark paper. Two blind people accidentally mixed up eight pairs of socks. How can each of them get back two pairs of black socks and two pairs of white socks?
Unpack each pair of socks, one for each person.
There is a train from Los Angeles to new york at a speed of 15km/h, and another train from new york to Los Angeles at a speed of 20km/h ... If a bird starts from Los Angeles at the same time with two trains at a speed of 30 km/h, meets another train and returns, and flies back and forth in turn until the two trains meet, how long does the bird fly?
The railway from Los Angeles to new york is one kilometer long. Then it took A/( 15+20) hours for the two trains to meet, which is the time for birds to fly. So the distance a bird flies is the length of the railway from L.A. to new york, and the speed × time =30×A/35=6/7.
You have two jars, 50 red marbles and 50 blue marbles. Choose a jar at random and put a marble in the jar at random. How can we give red marbles the best chance to be selected? What is the exact probability of getting the red ball in your plan?
1/2 probability. Choose the ball first, then the jar. This jar has no effect on the color of the ball.
You have four jars containing pills, and each pill has a certain weight. The contaminated pill is the uncontaminated weight+1. You only weigh it once. How do you know which jar is polluted?
Take out 1 pills from jar 1, 2 pills from jar 2, 3 pills from jar 3 and 4 pills from jar 4. Weigh 10 pills, which are several times heavier than the normal weight, indicating that there is something wrong with the medicine in the No.2 can.
You have a bucket of jelly, including yellow, green and red. Close your eyes and grab two jellies of the same color. How many can you catch to make sure you have two jellies of the same color?
Four. Quantity > color category. Colors must be repeated.
9 For a batch of lamps numbered 1 ~ 100, all switches are turned on, and the following operations are carried out: turn them on in the opposite direction every multiple of 1; A multiple of 2 toggles the switch in the opposite direction again; A multiple of 3 turns the switch in the opposite direction again ... Q: Finally, the number of lights in the off state.
There are 10 lights, namely 1, 4, 9, 16, 25, 36, 49, 64, 8 1, 100. Because every prime number can be divisible by 1 and itself, the prime number light is on. Let a composite number be divisible by n, and n must be an even number. For the composite number other than one party, it will be switched on and off for n times, that is, even times, and the light will remain on; The square number listed above was only switched N- 1 times, so the light went out.
10 A group of people held a dance, each wearing a hat. There are only two kinds of hats, black and white, and there is at least one kind of black. Everyone can see the color of other people's hats, but not their own. The host first shows you what hats others are wearing, and then turns off the lights. If someone thinks he is wearing a black hat, he will slap himself in the face. The first time I turned off the lights, there was no sound. So I turned on the light again and everyone watched it again. When I turned off the light, it was still silent. I didn't get a slap in the face until I turned off the light for the third time. How many people are wearing black hats?
There are three people wearing black hats. Suppose there are n people wearing black. When N= 1, the person wearing black can determine that he is black when he sees that everyone else is white. So when the lights are turned off for the first time, there should be a sound. It can be concluded that N> 1. For everyone who wears black, he can see the black hat of N- 1 and assume that he is white. But after waiting for N- 1 times and no one hits himself, every black person can know that he is black. So when the lights were turned off for the nth time, n people hit themselves.
1 1 two rings with radii of 1 and 2 respectively. The small circle goes around the big circle. How many times does the small circle turn by itself? If it is outside the big circle, how many times does the small circle turn by itself?
No matter inside or outside, the small circle turns twice.
12 if every three empty beer bottles can be exchanged for one beer, and someone buys 10 beer bottles, how many beer bottles can he drink at most?
Drink 10 bottles, nine empty bottles for three bottles of beer (there are four empty bottles after drinking). You can change 1 bottle of beer after drinking these three bottles (there are two empty bottles after drinking).
At this time, he has two empty bottles. If he can borrow an empty bottle from the boss first, he can make up three empty bottles and exchange them for a beer. After drinking this bottle of wine, he can return the empty bottle to the boss.
So he can drink10+3+1+1=15 bottles at most.
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Puzzle 1 (Pirate Gold Coin)-Pirate Gold Coin
After five pirates robbed 100 gold coins, they discussed how to distribute them fairly. They agreed on the distribution principle is:
(1) Draw lots to determine each person's distribution sequence number (1, 2, 3, 4, 5);
(2) Pirates who draw lots. 1 Propose a distribution plan, and then five people will vote. If the plan is agreed by more than half of the people, it will be distributed according to his plan, otherwise 1 will be thrown into the sea to feed sharks;
(3) If 1 is thrown into the sea, No.2 puts forward the allocation plan, and then four people are left to vote. If and only if more than half of the people agree, they will be allocated according to his proposal, otherwise they will be thrown into the sea;
4 and so on.
Assuming that every pirate is extremely intelligent and rational, they can make strict logical reasoning and rationally judge their own gains and losses, that is, they can get the most gold coins on the premise of saving their lives. At the same time, assuming that the results of each round of voting can be implemented smoothly, what distribution scheme should the pirates who have drawn 1 put forward to avoid being thrown into the sea and get more gold coins?
1:96 2:0 3:0 4:2 5:2
First of all, when voting on the proposal of 3, 4 will support 3, because otherwise he will die against 5.
Therefore, if 1 2 dies, the scheme of 3 must be 100, 0, 0, and it will be supported by 3 and 4. At this time, the payoffs of 4 and 5 are 0, so 1 2 can bribe 4 and 5 to get support.
At the same time, the expected return of 3 is 100, and he will be desperate to oppose 1 2.
And if 1 dies, the scheme of 2 must be 98,0, 1, 1, and it will definitely pass.
Therefore, the optimal scheme of 1 is 96,0,0,2,2, which will definitely pass.
In fact, 98, 0, 0, 1, 1 are also possible, and they may all pass (depending on the mood and cruelty of 4 and 5).
Puzzle 2 (guessing cards)
Mr. S, Mr. P and Mr. Q know that there are 16 playing cards in the desk drawer: hearts A and Q, 4 spades J, 8, 4, 2, 7, 3 flowers K, Q, 5, 4 and 6 diamonds A and 5. Professor John chooses a card from 16 card, tells Mr. P the number of points in this card, and tells Mr. Q the color of this card. At this time, Professor John asked Mr. P and Mr. Q: Can you infer what this card is from the known points or colors? So, Mr. S heard the following conversation:
Mr. P: I don't know this card.
Mr q: I know you don't know this card.
Sir: Now I know this card.
Mr. Q: I know that, too.
After listening to the above conversation, Mr. S thought about it and correctly deduced what this card was.
Excuse me: What kind of card is this?
The first sentence of p means that the number of points is one of a, q, 5 and 4.
Q: The first sentence indicates that the color is hearts or diamonds.
The second sentence of p means it is not a.
The second sentence of q can only be box 5.
Answer: Box 5
Puzzle 3 (burning rope problem)
It takes 1 hour to burn an uneven rope from beginning to end. Now several ropes are made of the same material. How to time an hour and fifteen minutes by burning rope?
Take three ropes.
First light both ends of the first root and light one end of the second root at the same time. (t=0)
When the first one burns out, light the other end of the second one. (t = 30 minutes)
When the second root burns out, light the two ends of the third root. (t = 45 minutes)
When the third root burns out, t = 75 minutes.
Problem 4 (Table Tennis Problem)
Suppose there are 100 ping-pong balls arranged together, and two people take turns to put the balls in their pockets. The winner is the person who can get the100th table tennis. The condition is: the person who holds the ball must take at least 1 at a time and not more than 5 at most. Q: If you are the first person to take the ball, how many should you take? How can I take it in the future to ensure that you can get the100th table tennis?
Take four first.
Then if the opponent takes 1 5, I will take 5 1. So in any case, the number of balls left is 6n, N minus 1. Finally, I just got six balls, and then I won.
Puzzle 5 (drinking soda)
1 yuan a bottle of soda, drink two empty bottles for a bottle of soda, Q: You have 20 yuan money, how many bottles of soda can you drink at most?
39 bottles
20->； 10->； five
Take four bottles for two bottles, another bottle, this empty bottle and 5-4 empty bottles for another bottle. 20+ 10+5+2+ 1+ 1=39
Puzzle 6
Three hunters led a black bear and two brown bears across the river.
The boat is so small that it can only carry two people, or two bears, or one bear across the river at a time.
All three hunters can row a boat. Black bears are trained by hunters to row boats.
But once the number of bears exceeds the number of people, bears will eat people.
How can I cross the river safely?
The black bear took a brown bear across the river first, and then rowed back to take another brown bear across the river. When the black bear rowed back, two tearful people crossed the river, a hunter brought a brown bear back, a hunter brought a brown bear back, and the black bear rowed back twice and brought two brown bears across the river.
Puzzle 7 (Guigu Kaotu)
Sun Bin and Pang Juan are both disciples of Guiguzi; One day, the ghost came up with a problem: he chose two different integers from 2 to 99, told Sun the product and told Pang the sum.
Pang said: I'm not sure what these two numbers are, but I'm sure you don't know what these two numbers are either.
Sun said: I really didn't know at first, but after listening to your words, I can confirm these two figures now.
Pang said, since you put it that way, I know what these two numbers are.
What are these two numbers? Why?
There is (4, t), where t = 7, 13, 19, 23, 3 1, 37, 43, 53, 6 1, 73, 79, 83, 9/kloc-.
Puzzle 8 (Puzzle)
It is said that someone gave the proprietress of a restaurant a difficult problem: this person knew that there were only two spoons in the shop, which could scoop 7 ounces of wine and 1 1 ounce of wine respectively, but forced the proprietress to sell him 2 ounces of wine. Smart proprietress is also unambiguous. She used these two spoons to hold the wine, turned it upside down and actually measured out 2 ounces of wine. Can you be smart?
Fill up 7, pour it into 1 1, fill it up again, and fill it up to 1 1. At this time, there are 3 left in 7.
Empty 1 1, pour 3 of 7 into 1 1, and then fill 7 into 1 1. At this time 1 1 Yes 10.
Fill it up with 7, and it will be 1 1, and there will be 6 left in 7.
Empty 1 1 again and pour 6 out of 7 into 1 1.
Fill it up with 7 to 1 1. At this time, there are 2 left in 7.
Puzzle 9 (King and Prophet)
Before going to the execution ground, the king said to the prophet, "Aren't you good at predicting?" Why can't you predict that you will be executed today? I'll give you a chance, and you can predict how I will execute you today. If your prediction is right, I will let you take poison to death; Otherwise, I will hang you. "
But the wise prophet's answer made it impossible for the king to execute him anyway.
How did he predict it?
You won't poison me. "
Puzzle 10 (strange village)
There are two strange villages somewhere. People in Zhangzhuang lie on Mondays, Wednesdays and Fridays, while people in Licun lie on Tuesdays, Thursdays and Saturdays. On other days, they tell the truth. One day, Wang Congming from other places came here, met two people and asked them questions about the date. Both of them said, "The day before yesterday was the day when I lied."
If the two people asked are from Zhangzhuang and Licun, what day is it?
It can also be exhaustive.
Monday.
Puzzle 1 1 (weighing the ball)
There are 12 balls and a balance. Now we know that only one of them is different in weight from the others. How can we find the ball after weighing it three times? Note that this problem does not indicate whether the weight of the ball is light or heavy, so it needs careful consideration. )
Firstly, it is proved that if three balls P 1, P2, P3 are satisfied, or P 1 is heavy, or one of P2 and P3 is light, and there are two standard balls, then the one with different mass can be found by the balance. In fact, if P 1 and P2 are compared with standard balls, P3 is lighter; If the sum of P 1 and P2 is greater than the standard ball, P 1 is heavier; If P 1 and P2 are smaller than the standard ball, P2 is lighter. Similarly, P 1, P2, P3 satisfy that either P 1 is light or P3 P2 is heavy, and non-standard balls can be found at one time.
Divide into three batches (marked as group A, group B and group C), with 4 in each batch, and weigh two batches of A and B.. If it is balanced, balls with different qualities are in Group C, and they can be found twice (compare two balls with standard balls first; If it is balanced, compare one of the remaining two with a standard ball; If it is not balanced, compare one with the standard ball. If it is unbalanced (it may be assumed that Group A is lighter than Group B), then Group C is the standard ball. Arrange a and b as follows
1234
A○○○
B○○○
Take A 1, A2, B1(Group A') and A3, A4 and B4 (Group B') and weigh them on both sides of the balance respectively. If group A' is lighter than group B', either A 1, A2 is lighter or B4 is heavier. From the previous proof, the third weighing can find out the different quality. If Group A is heavier than Group B, either B 1 is heavier or A3 and A4 are lighter, you can also find the one with different quality. If it is balanced and B2 and B3 are heavier, you can find the heavier two by putting them at both ends of the balance.