This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 1

2010 German National Olympiad, 3
Tags: combinatorics , set , infinite set , book , infinity
An infinite fairytale is a book with pages numbered $1,2,3,\ldots$ where all natural numbers appear. An author wants to write an infinite fairytale such that a new dwarf is introduced on each page. Afterward, the page contains several discussions between groups of at least two of the already introduced dwarfs. The publisher wants to make the book more exciting and thus requests the following condition: Every infinite set of dwarfs contains a group of at least two dwarfs, who formed a discussion group at some point as well as a group of the same size for which this is not true. Can the author fulfill this condition?