At a cocktail party with at least t

At a cocktail party with at least two people, there are two that know the same number of party
attendees.
Solution In a group of N people, a person may have 0, 1, 2, ..., N − 1 friends. Assume to the
contrary that all N people have different number of friends. Then for each number in the sequence
0, 1, 2, ..., N − 1 there must be a person with exactly this number of friends. In particular, there is
at least one with N − 1 friends. But, if so, all others have this person as a friend, implying that
there is no one with no friends at all. Therefore, the only possible numbers of friends come from the
shortened sequence: 1, 2, 3, ..., N − 1. By the Pigeonhole Principle, there are at least two with the
same number of friends, so that our assumption that this is not true proved wrong, thus it must be
indeed true.

ผลลัพธ์ (อังกฤษ) 2:

At a Cocktail party with at Least Two people, know that there are Two of the Same Number party
attendees.
Solution In a Group N of people, a person May have 0, 1, 2, ..., N - 1 friends. Assume to the
contrary that all people have different N Number of friends. Then for each in the Sequence Number
0, 1, 2, ..., N - 1 there must be a person with exactly this Number of friends. In particular, there is
at Least one with N - 1 friends. But, if so, all others have this person as a friend, implying that
there is no one with no friends at all. Therefore, the only possible Numbers of friends Come from the
shortened Sequence: 1, 2, 3, ..., N - 1. By the pigeonhole Principle, there are at Least Two with the
Same Number of friends, so that our assumption that. this is not true Wrong proved, thus it must be
true indeed.

ผลลัพธ์ (อังกฤษ) 3:

At a cocktail party with at least, two people there are two that know the same number of Party
.
attendees Solution In a. Group of N people a person, may have 0 1 2,,,..., N − 1 friends. Assume to the
contrary that all N people have different. Number of friends. Then for each number in the sequence
0 1 2,,,..., N − 1 there must be a person with exactly this number. Of friends, In particular.There is
at least one with N − 1 friends. But if, others, so all have this person as, a friend implying that
there is no. One with no friends at all. Therefore the only, possible numbers of friends come from the
shortened sequence 1 2 3:,,,,, N... Signed 1. By the, Pigeonhole Principle there are at least two with the
same number, of friends so that our assumption that this. Is not true, proved wrongThus it must be
indeed true.
.