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How many chains are there?

Source: Austrian Mathematical Olympiad 1998, Part 2, D2, P1

June 29, 2011
combinatorics proposedcombinatorics

Problem Statement

Let MM be the set of the vertices of a regular hexagon, our Olympiad symbol. How many chains ∅⊂A⊂B⊂C⊂D⊂M\emptyset \subset A \subset B \subset C \subset D \subset M of six different set, beginning with the empty set and ending with the MM, are there?
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