Star Wars Mini Games

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answer is to hear the man behind the top two people have said that the \Then that person will be the middle of the following reasoning: \been wearing a black hat, and now he does not know, on that I was wearing white hat this assumption is wrong, so I wear a black hat. \his white hat assumption is wrong, so he concludes, wearing his black hat.

we put this issue into the following form to promote:

\head and wore a cap. everyone can not see the color of his hat, and everyone could see his head in front of him all hat colors, but can not see anyone behind the head in his hat color. now starting from the last man, asked him if he knew his hat color, if he answered not know, they continue to ask the person in front of him. straight question, then there must be a person who knows his own hat color. \

of course, assume that a number of conditions:

1) First of all, hats must be greater than the total number of people, or are not wearing a hat.

2) \everyone knows everyone knows everyone knows it, and so on and so on. However, in this condition of \This information can be as above, specifically the classic form, list the number of each color hat

\is

\number of people may not know,

\The last row of people do not know until the last ─ ─ start to ask him to answer before he found no one else asked, did he know his last. Goes on in this post some time when I was out of question I will just write, \the.

3) the rest of us do not wear the hat of course, were hidden, and the ranks of people who do not know what hat are left.

4) all are not color blind, not only no, but as long as the two colors are different, they were able to come out. Of course they have very good eyesight, can see the front of the arbitrary distances. They are extremely intelligent, logical reasoning is excellent. All in all, as long as the theory was derived under the logic out, they must be derived out. On the contrary, if they could not push the color of a hat on his head, no one will try to guess or cheat peek ─ ─ I do not know as I do not know.

5) behind and in front of people can not whisper or play signal.

,Arizona Diamondbacks Hats, of course, not all of the pre-conditions can be given a reasonable topic. For example there are 99 black-hat,Houston Astros cap, 99 white-hat, two individuals, no matter how worn, can not anybody know the color of a hat on his head. In addition, as long as not only one color hat, only one person in a team, that person is not to say the color of his hat.

but following these questions are reasonable questions:

1) 3 顶 red cap, four black hat, white hat 5 and 10 individuals.

2) 3 顶 red cap, four black hat, white hat 5 and 8 individuals.

3) n black cap, n-1 white hat, n individuals (n> 0).

4) 1 顶 color of a hat, two hat colors 2, ... ..., 99 color 99 hats, 100 color 100 caps, a total of 5000 individuals.

5) has three colors of red yellow and green label each one two three, but do not know what specific color is a few top 6 individuals.

6) who do not know how many people (at least two) in a row, with white and black hats, each hat fewer than the number of 1.

we can not look at me first, following the analysis of these issues to try and make it.

According to the above three white hat black hat 2 do when the reasoning, then 10 people can be exhausted us, let alone 5,000 people had. But 3) the n is the number of abstraction, to consider how to solve this problem,cheap mont blanc pen, to solve the problem a lot of good in general.

Suppose now that individuals have n wear a hat, and asked that the person at the end of the hat on his head is the color, when he will answer \It is clear that he saw in front of only n-1 individuals wearing a white cap when possible, because then all the n-1 顶 white hat have been used up, in his own mind can only withstand the black hat, just in front of a black

hat, he can not rule out the possibility of head is black hat ─ ─ even if he saw all the black hat in front of everyone, he may be wearing a black top hat section n .

Now suppose that the last person the answer is \According to the last side who answer, he can infer it? If he sees are white hat, he can immediately conclude that his wearing a black hat ─ ─ If he wore a white cap, then the last one should see a white hat,wholesale Boston Red Sox cap, he asked him on the answer \know \However, if people see in front of the penultimate at least one black hat, he can not make judgments ─ ─ wearing a white hat he could, but his black hat in front of those who made the last answer \wearing a black hat.

this reasoning can continue, but we have seen the signs. The last person you can say \This is the crux of all hat colors!

if the last person to answer \where? Not somewhere else, only in the penultimate man his head. This reasoning continues, for each individual queue becomes:

\determine their own wearing a black hat, so if I see in front of all those who wear the white hat, I must wear my head to see that the man behind the black top hat. \What man in front of the hat not see, you see the black hat goes without saying, so if everyone behind him said, \the people behind him will see a black hat ─ ─ only the first one of that top of his head. Fact is quite clear, the first to say what color hat on his head the man is from the first few teams played the first people who wear black hats, that is, from the team that first saw the ending from the front all wearing White hat people.

This reasoning may suggest the flavor a bit circular, because in that part of reasoning includes \dangerous. But in fact there are no circular argument, which is similar to the reasoning of mathematical induction, each person's reasoning is based on his reasoning behind those people, rather

for the last one, he is no one behind , so his reasoning is not dependent on other people's reasoning to be established, is summarized in the first inference. Little reflection, we can change the above arguments have a variety of colors suitable for any inference:

\invisible from the first color of the hat that people can immediately and proof of this argument to the same judge,mont blanc pen wholesale, he is wearing the color of the hat. Now all the people behind me are answered do not know, so behind me The people saw this color hat. if in front of me I can not see the color of the hat, then I must be wearing the color of the hat. \reasoning is simple: \1) things became apparent, three red hats, four black hat, five 10 people wearing white hats, the color of each queue at least all that there is one, so from the team since the first ending in a color invisible hat the people will be able to conclude that he was wearing the color of the hat, by this point we can see, most asked the first few teams starting from the third person, it should be answered \starting from the first few teams who can only see a third two hats, so up to see the two colors, if the people are behind him to answer \on the wearing of a certain kind of see the color of his hat.

Question 2) is the same, three red cap, four black hat, five individual wearing a white hat to 8, then the queue must have at least one white hat, because the other colors add up to a total of only seven, So the queue will be answered \

question 4), a little large, but the truth is and 2) the same. 100 kinds of colors of 5050 to 5000 people wearing hats, the color of the hat in front of the number of 99 is 1 + ... ... +99 = 4950, so the queue must have the first one hundred kinds of colors of hats (at least 50), so if your The people behind the answer \

As for 5), 6) \people in a row, with white and black hats, each hat fewer than the number 1 \

final point to note is that we just proved above, if we can cap the number of colors and determine the number of queues in the queue at least a certain color of the hat, then we One can determine the color of the hat on his head. If all the people behind the answer \But this does not mean that he must ask the answer \For example, in question 2), if the queue is as follows: (arrow indicates the direction of the queue human face down)

vain black dark red red →

then end of the first in the team One can immediately answer is that white hat on his head because he saw all three and four black hat Red Hat can only be left to his own wearing white caps.相关的主题文章：



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