Logical thinking ability for doing math problems can't be cultivated and developed at once, it needs a long-term training process. The cultivation of logical thinking ability should be exercised by doing problems. The following math application problem is to train everyone to do it with assumptions, and the answers we give later are also answered with assumptions. This paper is a few main problems.

1. There are two people, A and B, in which A only tells lies and doesn't tell the truth. B only tell the truth, not lies. But when they answer other people's questions, they just nod and shake their heads to show that they don't talk. One day, a man was faced with two roads: Road A and Road B, one leading to the capital and the other to a small village. At this time, there are two people standing in front of him, A and B, but he doesn't know whether this person is A or B, and he doesn't know whether nodding means "yes" or "no". Now, he must ask a question before he can determine which road leads to Beijing. So, how should I ask this question?

Xiao Wang, Xiao Zhang and Xiao Zhao are good friends. One went into business, one was admitted to a key university, and the other joined the army. In addition, they also know the following: Xiao Zhao is older than the soldiers; College students are younger than Xiao Zhang; Xiao Wang's age is different from that of college students. Please infer which of these three people is a businessman. Who is a college student? Who is the soldier?

3. A, B and C are doing their homework together, and there is a difficult math problem. When all three of them said their solutions, A said, "I made a mistake." B said, "A did the right thing." C said, "I was wrong." Ding read their answers, listened to their opinions and said, "One of you three is right and the other is right." Which of them did the right thing?

Xiao Li bought a pair of beautiful shoes. None of her classmates have seen it, and everyone guessed that Xiaohong said, "The shoes you bought won't be red." Cai Xiao said, "The shoes you bought are either yellow or black." Xiaoling said, "The shoes you bought must be black." At least one of these three people's views is correct and at least one is wrong. What color are Xiaoli's shoes?

Ms Zhao bought some fruits and snacks to visit a friend. Who knows, these fruits and snacks were stolen by his son, but she doesn't know which one. Therefore, Zhao Nvshi was very angry and questioned his four sons who ate fruits and snacks. The boss said, "I was eaten by the second child." The second said, "The fourth stole it." The third said, "I didn't steal it anyway." Old four said, "Old two is lying." Only one of the four sons told the truth, and the other three were lying. So, who stole these fruits and snacks?

1. This person only needs to stand on either road of A and B, and then ask one of them, "If I ask him (the other one of A and B) if this road leads to Beijing, what will he answer?"

If a and b both shake their heads, they will go this way; If two people nod, they will go the other way.

Xiao Zhang is a businessman, Xiao Zhao is a college student and Xiao Wang is a soldier. Suppose Xiao Zhao is a soldier, which contradicts the condition that Xiao Zhao is older than a soldier in the title. Therefore, Xiao Zhao is not a soldier. Suppose Xiao Zhang is a college student, which contradicts the title "College students are younger than Xiao Zhang", so Xiao Zhang is not a college student. Assuming that Xiao Wang is a college student contradicts the condition that Xiao Wang's age is different from that of college students. Therefore, Xiao Wang is not a college student. Therefore, Xiao Zhao is a college student. According to the conditions, it is bigger than a soldier, a college student is younger than Xiao Zhang, Xiao Wang is a soldier and Xiao Zhang is a businessman.

Suppose c is right, then both a and b are wrong. In this way, A is right, B and C are wrong, which meets the requirements. So, c did the right thing.

4. Suppose Xiaoli's shoes are black, then all three views are correct and do not meet the meaning of the question; Assuming that it is yellow, the first two views are correct and the third view is wrong; Suppose it is red, then three sentences are wrong. So, Xiaoli's skirt is yellow.

It was the third child who stole the fruit and snacks, and only the fourth child told the truth. Assuming that the eldest, the second, the third and the fourth are telling the truth, if they contradict the meaning of the question, they can get the answer.