How to break into a math book

"Computer Principles" is the hint.Tu Hua looked at the letters spelled out with the colors of the book, and instantly understood them.

[Q_E] in the first line is actually the first row of letter keys on the computer keyboard, and [AS_] and [Z__] are the second and third rows of the keyboard respectively, so the correct order should be:

【QWE】

【ASD】

【ZXC】

The letters in the four spaces below are W, D, X, and C.Tu Hua hurriedly took some books with white covers from the side, and spelled out the remaining four letters in the spare red part.

The moment he finished the work, the entire wall of books began to change crazily, and the colors of the spines of all the books were flickering and changing, and finally formed a sentence on the wall: [D button is next to E button].

Fourth message!

So far, they have obtained a total of four pieces of information about the 6 buttons at the door: button A is to the left of button B; button B is the third to the right of button C; button C is to the right of button D; button D is next to button E .

According to the first two pieces of information, they have basically determined the positions of A, B, and C, and the third piece of information says that C is on the right of D, which proves that D must be in front of C.And now they got another piece of information, D is next to E, which proves that E is either one place in front of D or one place behind D.

That is to say the first button is either D or E.

The answer is ready to come.What is required in the rules is to select the button that is not mentioned in all the information. If the 6 buttons are sorted with capital letters, the only button that is not mentioned in A, B, C, D, E, and F is the F button. up.If the button not mentioned is the correct button, then the next piece of information must have nothing to do with F, which means it will complement the sequence of the other five buttons.

Tu Hua faintly felt a little excited, and wanted to find the last reminder message quickly.

The two quickly left the study and went to other floors to search.This old castle is simply terrifying. After they searched all ten floors panting, they still haven't found the fifth clue.

Wang Boyu honestly wanted to search again, but Tu Hua felt something was wrong.Although the last prompt is indeed more difficult than the first four in terms of probability, but the first four messages are very obvious, it is the kind of abnormality that can be seen at a glance, and the fifth message should be as easy as the first four Only to be discovered.

But other places in the castle are very normal. There is nothing in the room except furniture, and the upper floors are even a bit perfunctory, and the furniture is not even placed.

So where should the last message be?

The two returned to the first floor again, and saw the young NPC in this level cooking instant noodles again.

Tu Hua looked at him in astonishment: "Is cooking instant noodles only set in your program?"

The NPC gave him a blank look: "It's been half a day, can I be hungry again?"

Wang Boyu leaned on the door frame and looked in: "I'm hungry too."

The NPC ignored him, and sat at the dining table with a bowl of instant noodles sucking.Tu Hua stared at him meaningfully for a while, and said, "Is there something you are hiding from me?"

The NPC looked up at him: "What are you hiding from you?"

Tu Hua smiled, reached out and took out a few playing cards from the NPC jacket pocket: "What is this?"

The NPC quickly reached out to grab it, with an angry expression on his face: "Why are you still taking things out of other people's pockets!"

Tu Hua flipped through the cards indifferently, and then returned them to the NPC: "Didn't you tell me to look for clues in the castle? For me, you are also something in the castle, so... I think the last one The clue is in you."

Although this NPC looks a bit ambiguous, first it frightened Huahua, and later said that it needs the rescue of the challenger, but any NPC setting in the level is meaningful, and he is not used too abruptly.

So Tu Hua watched him carefully for a while, trying to find clues on him, and sure enough, he soon found the playing cards in his coat pocket.An NPC carrying playing cards?If he said that he had no conspiracy, no ghost would believe it.

Obviously, the IQ program of this NPC was not set up very well. Under Tu Hua's coercion and lure, he confessed after a while: "That's right, the last reminder is here."

"However, it's not that easy for you to get it." He said, and he showed those playing cards.

There are 6 playing cards in total, two K, a 4, a 2, an A and a Q.He shuffled the order of the six playing cards and put them on the table, then said: "Here are six cards, two of which are kings. You only have one chance to turn over two cards at once."

"The card you turn over must be the same as the prediction you made in advance. Of course, the prediction is not made casually." The NPC is proud, "You only have two choices, either predict that at least one of these two cards is a K; or Predict that there is no K in these two cards. That is, you choose one of these two possibilities, and the card you turn over must be the same as the possibility you predicted in advance."

"If you do, I'll give you the last reminder message."

Tu Hua understood what he meant. In fact, he was asked to make a choice between at least one of the two cards being a K and neither of the two cards being a K. The result of the flop must also be the same as the prediction.Among the six cards, two are kings. He can turn over two cards at a time, which means he is betting on what these two cards are.

This is actually a question of probability.Tu Hua must determine which of the two events "at least one of the two cards is a king" or "neither of the two cards is a king" is more likely to occur, and then he can make a choice.

If it is a probability question, this question is actually very simple.

王博宇很快就给出了分析概率的步骤和答案：“这道题其实很简单，总共只有6张牌，我们先给两张K牌编号为1和2，剩下的四张牌分别编号为3、4、5、6。一次抽取两张牌的话，这两张牌总共有15中组合方式。”

【1-2，2-3，3-4，4-5，5-6】

【1-3，2-4，3-5，4-6】

【1-4，2-5，3-6】

[1-5, 2-6]

[1-6]

“K牌在这15种数字组合中被表示为数字1和数字2，那么两张牌中至少有一个K的组合情况就有9种，而两张牌中一个K也没有的情况就是6种。”

“所以在15种情况的总和之下，两张牌中至少有一个K的概率就9/15也就是3/5，而一个K也没有的概率是2/5。”

Tu Hua nodded: "Yes, that is to say, if we choose to have at least one K, the probability of winning is relatively high."

The NPC seemed very proud: "So you chose to have at least one K?"

There are 6 face-up poker cards neatly placed in front of him. If Tu Hua chooses this situation, as long as he turns over 1 cards and there is [-] K, he can win and get the last prompt message up.But the problem is that this probability is not [-]% no matter how you calculate it.

Even if the probability of at least one king is higher, it does not prove that Tu Hua can definitely turn a king.If he is unlucky, it is very likely that he will not even get a K.

Wang Boyu also realized that something was wrong with the problem: "The probability is easy to calculate, but if you really hit it...is this gambling?"

The NPC shrugged innocently: "No way, the rules are like this."

Wang Boyu was annoyed: "But it's not fair!"

Seeing that the two were about to quarrel, Tu Hua suddenly stretched out his hand to hold Wang Boyu, beckoning him to be calm, and then calmly looked at the NPC: "I choose the option of at least one K."

The NPC looked at him with a smile: "Then please turn over the cards."

Tu Hua nodded, without hesitation at all, flipped through two cards randomly, the first one was a Q, and the second one was a K.

Wang Boyu was very excited: "You are amazing! How did you do it?! You are so lucky!"

The NPC was also a little surprised. His surprise was not that Tu Hua was able to find K. After all, the probability of K was objectively calculated, and it was indeed slightly higher.What really surprised him was Tu Hua's attitude.

Obviously for the challenger, this is a gamble, why can Tu Hua be so confident, as if... he has clairvoyant eyes and can see the hole cards?

The NPC was puzzled, and Wang Boyu was also at a loss.Tu Hua looked at the NPC with a smile, and reached out to him: "I've passed the level, please give me the hint!"

The NPC frowned, as if meeting the first bug in his life: "Tell me first... how did you determine that the card is a K?"

Tu Hua calmly said, "Damn it."

The NPC narrowed his eyes: "I don't believe it."

"Well, it's not a trick." Tu Hua smiled, "You give me the prompt first, and I'll tell you."

Driven by strong curiosity, this NPC who was full of instant noodles, he readily handed out the other note in his pocket, unfolded it, and saw that it was the correct message.

The NPC was itchy: "Can you tell me?"

Tu Hua handed the note to Wang Boyu, and then held up the K that he had turned over: "Look carefully at this card."

The NPC squinted his eyes and looked closer, his two eyes were almost crossed, and finally discovered the mystery.I saw an inaudible crease in the upper right corner of the K card.

Only then did he understand, and he roared furiously, "You cheated!"

That crease is indeed a mark made by Tuhua.When he first took out these cards from the NPC's pocket, he found that only 6 of the 2 cards had the same K.So he lightly folded the corner of one of the Ks casually, leaving a crease that only he could notice.

The NPC looked very deceived, and wanted to snatch the prompt back with a mournful face: "You cheated! How could you do that?!"

With an innocent face, Tu Hua retaliated against him in the same way: "The rules don't say that you can't mark in advance. There is no way, the rules are like this."

The NPC cried bitterly: "You cunning challenger! How can there be a challenger like you!"

Tu Hua calmly threw down the playing cards, walked to the gate with the reminder message, and compared the last message with other information: [There is a button between E and A].

Tu Hua pondered for a while, then looked at the six buttons at the door, with a clear smile on his face: "I know which button to press."