Two-person guessing problem analysis

Two-person guessing problem analysis

I accidentally saw a logical analysis question. After N hours of analysis, the analysis process is now recorded.

question

S 先生、P先生、Q先生他们知道桌子的抽屉里有16张扑克牌：红桃A、Q、4 黑桃J、8、4、2、7、3 草花K、Q、5、4、6 方块A、5。约翰教授从这16张牌中挑出一张牌来，并把这张牌的点数告诉 P先生，把这张牌的花色告诉Q先生。这时，约翰教授问P先生和Q 先生：你们能从已知的点数或花色中推知这张牌是什么牌吗？ 于是，S先生听到如下的对话：

P先生：我不知道这张牌。
Q先生：我知道你不知道这张牌。
P先生：现在我知道这张牌了。
Q先生：我也知道了。

听罢以上的对话，S先生想了一想之后，就正确地推出这张牌是什么牌。 请问：这张牌是什么牌？

From the topic analysis, it is obvious that this is a topic of finding unique data (cards) based on conditions. What Mr. P knows is the rank of the card, and what Mr. Q knows is the suit of the card . Then let's analyze the dialogue between Mr. P and Mr. Q one by one:

ideas

1. Mr. P: I don't know this card

   This condition is very simple, that is to remove all cards of the suit that are unique in point ( because Mr. P only knows the point ) ( only if the point is not unique, Mr. P will say I don't know this card ). Through this condition, we can easily get the following list ( with square brackets is the point card removed by the condition ):

   红桃：A、Q、4
   黑桃：[J]、[8]、4、[2]、[7]、[3]
   草花：[K]、Q、5、4、[6]
   方块：A、5

   That is to say, from Condition 1, we can infer from the point of view that the point of the card is one of A, 4, 5, and Q.

2. Mr. Q: I know you don't know this card

   This condition is actually very simple ( in fact, this is not the case, just to pretend to be a wave ). However, due to the location of this condition and the habit of personal thinking ( please ignore it automatically by experts ), it will be impossible to continue the analysis in condition 2.

   • Mistakes and reasons

   Since we are accustomed to numbering according to the conditions, progressive reasoning problems, then the chance will cause the scope to be further narrowed on the basis of condition 1. At this time, we will fall into the misunderstanding of this question: according to the suit, only spades can be removed, which will lead to the subsequent condition 3. Condition 4 is meaningless .

   • correct thinking

   In essence, by combining the word now in Condition 3 , we can guess ( just guessing, you should guess boldly to solve the problem, and verify carefully ) Condition 1 and Condition 2 are in a parallel relationship, that is to say, Condition 1 and Condition 2 are work simultaneously. In simple terms, it can be understood that condition 1 and condition 2 are said by Mr. P and Mr. Q at the same time, and there is no precedence . Since condition 1 and condition 2 work at the same time, we don't need to consider condition 1 when we consider condition 2 .

   To sum up, since Mr. Q starts from the suit and does not know the conclusion of Mr. P from the point of view, he can say that I know that you do not know this card , then it means that all points in this suit will have at least one other suit, that is, Says that there are no unique points in this suit that other suits do not have . Then, we can remove the suits with unique numbers, that is, remove spades and grasses . Get the following list ( with square brackets is the suit removed by the condition ):

   红桃：A、Q、4
   黑桃：[J]、[8]、[4]、[2]、[7]、[3]
   草花：[K]、[Q]、[5]、[4]、[6]
   方块：A、5

   • Summarize

   In fact, considering condition 2 alone, it is easy to filter out the two suits of spades and grasses, but because condition 2 is after condition 1, it is easy to enter a misunderstanding due to inertial thinking. In fact, the problem would be easier if condition 1 and condition 2 were swapped.

3. Mr. P: Now I know the card

   At this point, we need to combine the previous condition 1 and condition 2 to obtain the result to obtain the intersection, and the result is as follows:

   红桃：A、Q、4
   方块：A、5

   Furthermore, we analyze condition 3. Since Mr. P said that now I know this card, I can be sure that the value of the card is among the three points of 4, 5, and Q ( at this time, Mr. P knows, but what should Mr. S do? What should we do? So conditions are required. 4 ). Please note: If it is A, since the suit that Mr. P does not know is uncertain, Mr. P will not say that I know it .

4. Mr. Q: I also know

   Condition 4, which finally determines the uniqueness condition, is here! Mr. Q said that I also know it from the perspective of the color ( actually, this place is for the purpose of understanding the question, Mr. Q should not know, and everyone is welcome to correct me ).

   Since it can be uniquely confirmed from the perspective of suit and combined with the conclusion of conditional condition 3 ( the reason why it is not considered like condition 1 and 2 and condition 3 here is that Mr. Q uses: also, there is a sequence. I am guessing ), then we can confirm that the final card is:

   方块5

Summarize

The main difficulty of this question is the analysis of condition 2, avoiding the misunderstanding caused by thinking inertia.

In a continuous and stable environment, it will inevitably bring corresponding thinking inertia. The inertia of thinking has both advantages and disadvantages. The advantage is that it can speed up the communication efficiency between people in a stable environment, and the disadvantage is that it brings wrong conclusions.

When the environment changes (in the case of changing jobs, changing colleagues, changing leaders, etc.), we must be careful about the terrible impact of inertia of thinking.

The above is purely personal opinion, welcome to discuss together!