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The guests at the party

The guests at the party

Irene has been invited to a birthday party attended by a total of 12 people (including her) and only meets another one of the people at the party.

Josep, another attendee, only knows two others.

A third assistant, Griselda, knows three others and so on, so that eleven of the guests can be sorted so that each one knows a person more than the previous one, until they reach the number 11 person who knows all the assistants.

How many people know the twelfth and last guest?

We have to assume that if one person X knows another, Y, then person Y knows X.

Solution

We start with guest number eleven, who knows everyone. As Irene only knows one, it is he she must know.

Guest ten, who knows only 10, knows everyone (including the twelfth guest), except Irene.

He who knows only two knows eleven and ten and no one else.

Thus, successively, those who know most also know the twelfth, and none of those who know less know him.

In the end, it turns out that meet exactly 6 guests, which in the ordered list are those that go from 6 to 11.