Classic logical reasoning

I,
Mr. Q is playing games with Mr. S and Mr. P. Mr. Q writes a number each with two small pieces of paper. Both numbers are
Is a positive integer with a difference of 1. He pasted a piece of paper on Mr. S's forehead, and another on Mr. P's forehead. So,
Two people can only see the number on each other's forehead.
Q: Who of you can guess the number on your head?
Mr. s said, "I cannot guess ."
Mr. P said, "I cannot guess either ."
Mr. s said, "I still cannot guess ."
Mr. P said, "I cannot guess either ."
Mr. s still cannot guess; Mr. P cannot guess either.
Mr. S and Mr. P cannot guess three times.
However, for the fourth time, Mr. S shouted, "I know !"
Mr. P also shouted, "I know !"
Q: What are the numbers on the heads of Mr. S and Mr. P?

II,
There is a cell and three prisoners are in it. Because the glass is thick, three people can only see each other and cannot hear each other.
The voice of the other party ."
One day, the king thought of a way to give each of them a head wearing a hat, only to let them know the CAP
The child's color is either white or black, so they do not know what color they are wearing. In this case
The King announced the following:
1. Who can see that the other two prisoners wear white hats to release them;
2. Anyone who knows they are wearing a black hat will release them.
In fact, the king gave them black hats. Because they were bound, they could not see themselves. So the three of them
People stare at each other and don't talk. However, in the near future, mind a determined that he was wearing a black hat by means of reasoning. You want
How did he infer it?

III,
There is a very old village in which there are two kinds of people: red eyes and blue eyes.
The difference is that no one knows the color of his eyes before a child is born. There is a wide area in the middle of the village.
The scene is where villagers gather. Now there are only three people in this village.
Three places of residence. In this village, one rule is that if a person can know the color of his eyes and
If he commits suicide, he will go up to heaven. These three men cannot tell each other the color of their eyes in words, nor can they use any
How to remind the other party of the color of the eyes, and the mirror cannot be used,
Water and other reflective substances to see the color of their eyes, of course, they are not blind, they can see each other
But cannot tell him! They can only think about it, so they come to the square early every morning.
Sitting face to face, thinking about the color of your eyes, day by day
There was no progress at all until one day, a foreigner came to the square and said a word, changing him.
He said, at least one of you has a red eye. Then I leave. These three have listened.
Then, they sat down at night and went back to bed. The next day
I came to the square and sat down for another day. That night, two people successfully committed suicide! The third day, when the last person
When I came to the square, I saw that the two men had not come. I knew they had successfully committed suicide, so he also went back.
A successful suicide!
Based on the above, please show the colors of the eyes of three people and be able to tell the reasoning process!

IV,
The two houses are next to each other. The three switches in one house control the three lights of the other house.
You can only enter the two houses once. How can you determine which switch controls the lamp?

V,
The following nine vertices are arranged:
...
...
...
How to use four straight lines to connect these nine points (the four straight lines are required to be continuous)

VI,
Note: coins in American currency include 1 cent, 5 cent, 10 cent, 25 cent, 50 Cent, and 1 dollar. Let's take a look at the text and challenge the limits of your logical reasoning.
A store was just open, with only three male customers and a female shopkeeper in the store. When the three men stand at the same time
When you get up and pay the bill, the following situations occur:
(1) Each of the four has at least one coin, but neither is a coin with a nominal value of 1 cent or 1 dollar.
(2) none of the four can open any coin.
(3) A man named Lu has the largest amount to pay, and a man named Mo has the second to pay,
A man named Ned has to pay the minimum amount of the bill.
(4) No matter how much a man pays the bills with his coins, the shopkeeper cannot clear the change.
(5) If the three men exchange coins in their hands, they can pay off themselves.
The Bill does not need to be changed.
(6) After the three men exchanged their values twice, they found that the coins in their hands were
None of the coins held share the same nominal value.
As things develop, the following situations occur:
(7) after the bill is paid off and two men leave, the men left behind will buy some sweets. This man
Shi could have used the remaining coins in his hand for payment, but the shopkeeper could not use the coins she holds to clear the change.
(8) so the man paid for the candy with a dollar bill, but now the shopkeeper had to pay all of her
I found him all the coins.
Now, please don't worry about how the shopaholics encountered troubles when looking for a fraction that day.
The dollar bill paid for the candy?
VII,
There is a river with hunters and wolves along the bank, and a man with two children. There is also a woman with two children,
If the hunter leaves, the wolf will eat all the people. If the man leaves, the woman will throw her two children to death,
If a woman leaves the same boat as above, only two people can be on the ship (only hunters, men, and women are allowed)
Rowing). Q: How can these eight people cross the river (both on the river side, the wolf is counted as one)