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Rebecca已解答第一題：
http://hk.knowledge.yahoo.com/question/question?qid=7013102600098

我已解答後兩題：
http://hk.knowledge.yahoo.com/question/question?qid=7013103000224

你的 5(a) 和 (b)：

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6.
In a group of five people, one can have no friend, or one friend, or two friends, or three friends, or four friends (be friends with everyone in the group). It looks like there are five pigeon holes (possible numbers of friends) but actually, if someone in a group has four friends, there cannot be anyone with no friends in that group. So there are only four pigeon holes: either zero through three friends, or one through four friends. Pigeons are five people of the group.

In my words, there are 5 people in total.

Case 1:
If there is a person who has no friend within this group.
Then the number of friends of the people in this group can either be 0, 1, 2, 3 (it cannot be 4, otherwise that person mentioned earlier would have a friend).
Five persons with 4 possible numbers of friends, then by pigeonhole principle, there must exists the same number of friends.

Case 2:
If there is no person who has no friend within the group.
Then the number of friends of the people in this group can either be 1, 2, 3, 4.
Five persons with 4 possible numbers of friends, then by pigeonhole principle, there must exists the same number of friends.

看：
http://hk.knowledge.yahoo.com/question/question?qid=7013103100005

http://hk.knowledge.yahoo.com/question/question?qid=7013103100169

http://hk.knowledge.yahoo.com/question/question?qid=7013103000224

http://hk.knowledge.yahoo.com/question/question?qid=7013102500175

http://hk.knowledge.yahoo.com/question/question?qid=7013103100004
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