Mathematical problems (logical reasoning) There are 2 suspect in the 1 murders, 4 witnesses, 1 witnesses: no one guilty. Witness 2: B is innocent. Witness 3: at least one of the 2 people in front is true. Witness 4: witness 3 lying! Only the witness speaks the truth with 4. Who is the murderer?

Explanation of "only witness 4 tells the truth"
The other people tell lies, that is, witness 1: A is not guilty. No! A is guilty; witness 2: B is not guilty. No! B is guilty; witness 3: at least one of the first two people is true. No! None of the first two people is true. All of them are false
The killers are a and B

Mathematical problems of logical reasoning
ABCDE five teams play a round robin (one match between any two teams), and each team plays a round robin in two football fields at the same time every day, and one football team has a round robin. The order of the round robin is ABCDE. On the first day, B vs. C, the second day, C vs. e, and the third day, B vs. D. which two teams are the two teams in the fifth day?

One day, team a is out of the round, and team B is known to be against team C, then there is another game that team D is against team E;
The next day, team B is out of the round, and team C is known to be against team E. then there is another game, a against team D;
On the third day, when team C is out of the round, and team B is known to be against team D, there is still a match between team a and team E;
On the fourth day, if team D is out of the round, the game will be held between a, B, C and E. A and E have passed, and C and E have passed. Therefore, B vs E and a vs C
On the fifth day, e finished the race, and there were still four teams left, a, B, C, and d. A, B, and d all competed, so on the fifth day, C played D, and a played B

A mathematical problem of logical reasoning
Teachers a, B and C teach Chinese, mathematics, history, biology, physics and chemistry respectively
(1) The chemistry teacher and the math teacher live together;
(2) Teacher a is the youngest of the three teachers;
(3) Mathematics teacher and teacher C are a pair of excellent national chess players;
(4) Physics teacher is older than biology teacher and younger than B teacher;
(5) The oldest of the three lives far away from the other two
What are the two courses taught by the three teachers?

A: mathematics, biology
B: Chinese, history
C: Physics, chemistry
(from 2 and 4, the age order of the three people is a, C and B
Five more, a and C live together
There are three. A teaches math
From 4, a teaches biology, C physics
And then from 1, we get C chemistry
The last remaining language, history is taught by B)

Lesson 6, question 8,
Among the 100 glass balls, one is heavier than the other 99, and the other 99 are equally heavy. Now another balance, at least how many times, will be able to find this overweight ball

5 times we only consider the worst case: 1, first divided into three groups: 33, 33, 34, with the balance called each of the two groups of 33, if balanced, then in the third group, if not balanced, then in the heavier group. 2, the worst case is the heavy ball in the third group

Solving problems with equations (2)
6-10 questions of synchronous exercises
analysis.
The first one: A, B and C, a and B from the east town to the West Town, C from the West town to the East Town, three people set out at the same time, on the way, C and B meet 2 minutes later and meet A. if every minute a line 50 meters, B line 60 meters, C line 70 meters. Then, B than a how many minutes to arrive in the West town?

Let's send the title!

A workshop should process 50 parts per day according to the plan, and actually process 56 parts per day. In this way, not only the original planned task of processing parts is completed three days in advance, but also 120 more parts are processed. How many parts are actually processed in this workshop?

The actual use of X days to complete tasks, the original plan uses (x + 3) to complete tasks, the original plan uses (x + 3) to complete tasks, 56 × x-50 (x + 3) to complete tasks, 56 × x-50 (x + 3) = 120 (56 × x-50 (x + 3) is 56 × x-50 (x + 3) = 120 (56 × x-50 (x + 3) = 120 & nbsp; 56 x-50x-50 (x + 3) is 56 × x-50 (x + 3) = 56 (x + 50 (x + 3) = 56 (56 x + X + 50 (x + 50 (x + 3) = 56 (56 x + X + 50 (x + 50 (x + 50 (x + 3) = 120 (56 x + 50) (56 x + 50 (x + X + 50 (x + 50 (x + 50 (x + 3) = 120) (56 x + 50 (x + 50 (x + 50 (x + 50 (x + 3) = 120) (56 x + 3) = 120) (56 x + 50) (56 x + 56 nbsp; &X = 45; number of parts actually processed: 56 × 45 = 2520. A: 2520 parts were actually processed in this workshop

Lesson 1 DRAWER problem (1)
1. How many natural numbers can we take to ensure that the difference between at least two numbers is a multiple of 7?
2. From 1,2,3 Of these 12 numbers, take any 7 numbers, of which the difference is equal to 6. How many pairs are there at least?
3. The school bought several books of history, literature and art, and popular science, and each student borrowed two of them at will. How many students must have borrowed the same kind of books?
Hope to have an explanation
Thank you again!

There are 7 kinds of residuals divided by 7, so at least 8 times 2.1 pairs of (1,7) (2,8) (3,9) (4,10) (5,11) (6,12) are divided into 6 groups, so there are at least 2 pairs of 7 in the same group, so there is at least 1 pair of 3.7

Mathematical logic reasoning
1 / 9 = 0.111 (cycle)
9 * (1 / 9) = 0.999 (cycle)
So 1 = 0.999 (cycle)?
What's wrong?
Zihan

Because 1 / 9 is not the exact value expressed by 0.111 (cycle)
1 = 0.999 (cycle) is not wrong

Everyone can see the color of other people's hat, but can't see their own. The host first let everyone see what other people's hat is, then turn off the light, if someone thinks they are wearing a black hat, clap hands. The first time turn off the light, there is no sound Turn on the light again, and you'll see it again. When you turn off the light, it's still silent. Only when you turn off the light for the third time, can you hear the sound of crackling hands______ People wear black hats

If x = 1, the first time someone wearing a black hat sees that other people are all white hats, then they must be black hats. So it's time to clap. But the first time no one claps, it means that there are at least two black hats x = 2. The second time, if someone only sees that other people have only one black hat, they can judge that they are black hats, so they should clap

Seek the senior to solve several civil servants' logical reasoning problems~
1. A jewelry store was stolen and five staff members were arrested for trial. Suppose that among the five staff members, those involved in the crime will always tell lies and the innocent will always tell the truth. The five staff members have the following confessions respectively. Zhang said: Wang is the perpetrator. Wang said that he has committed a crime. Wang said: Li is the perpetrator. Li said that it was Zhao's crime. Zhao said that it was sun's crime. Sun did not say a word. Who is the perpetrator?
2. According to the statistics of the research results of a certain research institute in last year, no two researchers in the Institute published exactly the same number of papers; no one published exactly 13 papers; no one published more than or equal to the number of researchers in the Institute. If the above statistics are true, then which of the following conclusions must be true. (indefinite term)
A among the staff of the Institute, some did not publish a paper last year
B the number of researchers in the Institute shall not be less than 3
C the number of researchers in the Institute is no more than 13
If you can tell this kind of problem-solving skills better. Thank you very much

Zhang, Li and sun are the perpetrators. Zhang said: Wang is the perpetrator. Wang said that he has committed a crime. This sentence contradicts the known conditions, because the perpetrator can not tell the truth, so Wang is not the perpetrator. Even if Zhang said a lie, he is the perpetrator. So Li is the perpetrator, and sun is also the perpetrator

Mathematical problems (logical reasoning) There are 2 suspect in the 1 murders, 4 witnesses, 1 witnesses: no one guilty. Witness 2: B is innocent. Witness 3: at least one of the 2 people in front is true. Witness 4: witness 3 lying! Only the witness speaks the truth with 4. Who is the murderer?