2) Two Russian mathematicians meet on the plane. "If I remember correctly, you have three sons." Ivan said. "How old are they now?" "The product of their ages is 36," Iger said. "Their ages add up to today's date." Sorry, Edgar said a minute later, "You didn't tell me your son's age." "Oh, I forgot to tell you that my youngest son has red hair." "Oh, that's clear," Ivan said. "Now I know how old your three sons are."
3) 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?
Tip: The principle of judging pirates: 1. Life-saving; 2. Get as many gems as possible; 3. Kill as many people as possible.
4) Five prisoners caught mung beans in a sack containing 100 mung beans. They are 1-5 respectively. It is stipulated that everyone should catch at least one mung bean, and those who catch at most and at least should be put to death. And they can't communicate with each other, but when they catch it, they can find out the remaining number of mung beans. Ask them who has the best chance of survival. Tip:
1, are very smart people.
Their principle is to save people first, and then kill more people.
3, 100 don't have to finish it all.
4. If there is any duplication, it will be regarded as the largest or smallest and executed together.
5) The teacher's birthday is January B, and neither student knows the teacher's birthday. The teacher told A this value, and told B this value.
The teacher asked them if they knew when his birthday was.
March 4th March 8th June 7th September 1 September 5th 65438+February1,65438+February 2nd 65438+February 8th.
A said: If I don't know, of course B doesn't know. B said: I didn't know at first, but now I know. A said: Oh, I know that, too.
Please infer when the teacher's birthday is.
6) Mr. A went to a mysterious island and found that there were 60 people living on it. They can be divided into two types. The first kind of person (hee hee) tells the truth; The second kind of people (haha) all lie. But sometimes I accidentally make mistakes (that is, telling lies, haha telling the truth). Mr. A, who was trapped on the mysterious island, turned to people who were hee hee and haha for help.
At this time, hee hee and haha gave him a problem. These 60 people form a circle, and then everyone claims to be standing between Xi Xi and Haha. However, I found that both of them made mistakes! They lied unintentionally. At this time, one of them asked Mr. A, if he could guess how many people were hee hee and haha, he promised to help Mr. A escape from the mysterious island! Can you guess how many hee hee people and haha people there are?
* * Everyone has no marks of hee hee and haha, which can't be distinguished by the naked eye. You can only guess their number by what they said above.
7) A king has 1000 bottles of red wine, which he intends to open on his 60th birthday. Unfortunately, a bottle of red wine has been drugged, and anyone who touches it will die (even if he touches a drop) in less than a day. Because tomorrow is the king's birthday (assuming only 24 hours), he wants to find out the poisoned wine as soon as possible. So he ordered the guards to feed the prisoners on death row with wine. If there are "countless" death row inmates in the prison, you can have as many as you want, so how many death row inmates do you need to support you at least?
8) Coin problem
Now, there are 100 coins on the table in front of you, which are "men" in the sky and other coins are "flowers" in the sky, and then your eyes are blindfolded. You can't remember the location of all the coins. Now you try to divide these coins into two parts, so that each coin has the same number of coins that are "men" in the sky (the number of coins that are "flowers" in the sky need not be the same). Excuse me, how did you do it?
Of course, suppose you can't touch whether the coin in the sky is a "man" or a "flower" with your hands, and no one is there to remind you.
9) Among the 52 playing cards, shuffle the cards first, and then arrange them from left to right (all are open). Now you and your friends take turns to take cards, only one at a time, and each card can only be taken from the far left or the far right. After you get the card, you and your friends add up the number of cards you get (J, Q, K stands for 1 1, 12, 13), and whoever adds up the most numbers is the winner. The same number counts as the sum. If you are a pioneer, how do you make an unbeaten strategy?