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Islands and bridges

Source: Iberoamerican Olympiad 2009, problem 1

September 23, 2009
combinatorics proposedcombinatorics

Problem Statement

Given a positive integer n≥2 n\geq 2, consider a set of n n islands arranged in a circle. Between every two neigboring islands two bridges are built as shown in the figure. Starting at the island X1 X_1, in how many ways one can one can cross the 2n 2n bridges so that no bridge is used more than once?
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