Page's robot: "I don't know your number."
George's robot: "Needless to say, I knew you couldn't guess my number just now."
Page's robot: "I still don't know your number."
George's robot: "Needless to say, I know you still can't guess my number."
Page's robot: "I don't know your number yet."
George's robot: "Needless to say, I know you still can't guess my number."
Page's robot: "So I know your number."
So, what is the product of two numbers?
analyse
In order to satisfy the two conditions of "one digit" and "the sum of two digits is greater than 10", the effective digits can only be:.
If you guess the other party's number according to your own number, there is only one way to draw a conclusion directly: if your own number is 0, you can directly guess the other party's number is 0.
In other cases, only one range (or candidate number) can be obtained:
One person's own number, another person's number range.
Look at the first dialogue first.
According to the first sentence of Page Robot, it can be concluded that its number is not.
What about George's robot? Why can George's robot conclude that the other person can't guess his number before speaking? If George's number is 0, can it be concluded that the other party can't guess his number? The answer is: no. Because the other party includes it, and the other party (Page) can guess his (George's) number from it. Therefore, according to George's sentence, it can be excluded from George's digital "candidate list".
The first sentence of George's robot is the key and the breakthrough of the whole problem.
So, is it possible that Paige's number is?
Look down at the second dialogue:
If Page's number is, according to George's supplementary information in the first conversation, you should be able to guess George's number.
The reality is that after being excluded, Page's robot still can't guess George's number, so it can be excluded from Page's candidate number.
Note that George concluded that the other party "still can't guess" his number before Page spoke, indicating that according to George's own number, there is no candidate number for Page; Therefore, George's number should be less than or equal to.
So, is it possible that Paige's number is?
Look down at the third dialogue:
If Page's number is, then Page's candidate number is. The two have been excluded from the previous two conversations, but Page still can't guess George's number, which means that Page's number is not, but greater than or equal to.
George's third sentence shows that it infers from his own number that Page's number is not; Therefore, George's number is less than or equal to.
So, is it possible that Paige's number is?
The answer is yes. Please look at this sentence:
Draw inferences from George's three sentences: George's number range is:.
If the number of page robots is greater than or equal to, then more than one of these five numbers meets the requirements.
The paging robot can guess George's number this time. What does this mean? According to the number of pagerobots, only one of these five numbers meets the requirements.
Therefore, the number of page robots is 0, while the number of George robots is 0.
The product of two numbers is.
Refine and improve
Exclusion is a very important and commonly used method in logical reasoning.
A typical example is the problem of "liar, gambler and priest". One of the three people said, "I'm a liar."
We can infer (1) that he is not a liar; (2) He is not a priest; So he can only be a gambler.
In this topic, we applied the exclusion method from many angles many times, and finally locked the numbers of two robots.
An untrained person will be at a loss when confronted with such a problem. People who have studied logical reasoning can draw correct conclusions through their own efforts, which will be fun.