Posted in Տրամաբանական մանթեմ

տրամաբանական խնդիրներ

1. The smartest prince. The king wants his daughter to marry the three most intelligent young princes of the most intelligent, and thus the king's wise men prepare an intelligence test. The princes are sitting in one room and facing each other, displaying two black hats and three white hats. They are blind, with one hat placed on each head, the other hats hidden in another room.The king tells them that the first prince to remove the hat color without removing it or looking at it will marry his daughter. Wrong prediction will mean death. Then the brackets are closed. You are one of the princes. You see 2 white hats on the other prince's head. After a while you realize that the other princes are unable to cast the color of their hat or are not ready to guess. What color is your hat?
Note: You know your rivals are smart and want nothing more than to marry a princess. You also know that the king is the man of his word, and he has said that the test is a fair trial of intelligence and courage.

Solution: white. The king would not choose two white hats and one black hat. This would mean that the two princes would see one black hat and one white hat. You would be disadvantaged if you were the only prince wearing a black hat. If you were to wear a black hat, it would not take long for one of the other princes to decide that he was wearing a white hat. If a smart prince saw a white hat and a black hat, he would eventually realize 
that the king would never choose two black hats and one white hat. The prized prince, who sees two black hats, immediately knew that he was wearing a white hat. Therefore, if the prince can see one black hat, then he may have a case that he is wearing white. Therefore, the only fair test is that all three princes wear white hats. After waiting for some time just to make sure you can safely claim that you are wearing a white hat.

2. 100 Gold Coins Five pirates have acquired 100 gold coins and are forced to distribute loot. The pirates are all extremely smart, treacherous and selfish (especially the captain). The captain always offers loot distribution. All pirates vote in favor of the offer, and if half or more of the crew goes "A", the loot is split on the offer, as no pirate will want to take over the captain without superior force. If the captain fails to support at least half of his staff (which includes himself), he will resist arrogance, and all the pirates will turn to him.and make him walk the board. The pirates start again as the next captain. What is the maximum number of captains a captain can keep without risking his life?

 Solution: 98 The captain says he will take 98 coins, and one coin will give the third adult pirate and another coin the younger pirate. He then explains his decision in this way ... If there were 2 pirates, 2 pirates were the tallest, he would just vote in his favor and that would be 50% of the vote, so he obviously intends to keep all the money for himself. ​​3If he were a pirate, Pirate 3 would have to at least persuade another person to join his plan. Pirate 3 would take 99 gold and 1 coin to give Pirate 1. Pirate 1 knows if he doesn't vote for Pirate 3 then he gets nothing, so he's obviously going to vote for this plan. If there were 4 pirates, pirate 4 would give 1 dragon to pirate 2, and pirate 2 knows,
if he doesn't vote for pirate 4, he gets nothing, so he's obviously going to vote for this plan. Since there are 5 pirates, 1 & 3 pirates obviously voted better for the captain, or they face no choice or the risk of death.

3. Greek Philosophers One day three Greek philosophers found themselves under an olive tree, opened a bottle of Reticia, and began a lengthy debate on the "fundamental question". Why is there anything? After some time they started to mix. Then, one by one, they fell asleep. While the men were asleep, three rings above each philosopher completed their digestive process, throwing a gift at each philosopher's forehead, and flying
was coming out with a noisy "hammer." Perhaps the belly awakened the philosophers. As soon as they looked at each other, all three started laughing at the same time. Then one of them abruptly stopped laughing. Why?

Solution. If he (the most intelligent philosopher) had nothing in his head, then he would have realized that the second most intelligent philosopher would work quickly, that the third intelligent laughing would only laugh at the second clever philosopher, and thus the second clever philosopher would stop. laughing

4. Two Kids I randomly ask people if they have two children and if one is a boy born on Tuesday. After a long search, I finally find someone who answers yes. What is the probability that this man has two sons? Suppose you have an equal chance of giving birth and have the same chance of being born every day.

Solution: 13/27. If you think the answer should be 1/2, you would be wrong. If you knew which child is a boy (say, the youngest), you would be closer to the truth. But since the boy could be a smaller or older child, the analysis is more subtle. But what about Tuesday?

5. Monkey and Coconut Ten people land on a desert island. There they discover numerous coconuts and monkeys. During the first day, they collect coconuts and put them all in a community heap. After working all day, they decide to sleep, and the next morning they are divided into ten equal groups. That night a runaway wakes up hungry and decides to take his share early. After dividing the coconut, he finds that he is ten equal to one coconut. He also notices another coconut holding the monkey. So he tries to get the monkey coconut to evenly divide by 10. But when he tries to take it, the monkey chains him and kills him.Later another boatman wakes up hungry and decides to take his share early. On the way to Cocos, he finds the body of the first shipwreck, which pleases him, as he will now be entitled to 1/9 of the total heap. After dividing their nine heaps, he again cuts a single coconut and tries to pick up the slightly bloody monkey coconut. The monkey ties the second man on top and kills him. Each of the remaining ruins goes through the same process one by one until the 10th person who wakes up receives the whole heap for himself. What is the smallest amount of coconut in the pile, excluding the monkeys? Solution: 2519 Response Solution is 10,9,8,7,6,5,4,3,2,1 -1 -1 LCM (lowest total multiplier). The LCM will give the least number divided by all these numbers, and subtracting them will give us the coconut number that was originally there.

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