In a group of nine people, one person knows exactly two others, two people know exactly 5 others, and another 2 people know exactly 6 others. show that there are three people who all know each other

1, 2 and 5 all know each other.

Step-by-step explanation:

I will denote the people by numbers: 1 2 3 4 5 6 7 8 9

The following information is given in the question.

1 knows two others

2 knows five others

3 knows five others

4 knows six others

5 knows six others

Let's assume the worst case: They all know different persons, so it is difficult to find three people who all know each other.

1 knows 2 and 5

2 knows 1 3 4 5 6

3 knows 9 8 7 6 2

By now, 2, 5 and 6 are known to two people, and others are known to just one person.

4 knows 9 8 7 6 5 3

5 knows 1 2 4 7 8 9

As a result 1, 2 and 5 all know each other.

1 knows 2 and 5

2 knows 1 and 5

5 knows 1 and 2

The reason for this is that there are three groups:

1, (2,3) and (4,5)

As much as we try to separate the people that they know there are nine different persons and at least three of them will be spread to these groups in common.

good luck on your studies! : )

david edward.

in if you ask questions, the points are taken from your total and given to the one who answered it..

so if i have 30 points and i ask a question for 5 points, then when someone asks a question i will lose 5 points and the answerer earns 5

happy to