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How Many Such Sequences Exist?

Source: Irish Mathematical Olympiad - Paper 1 - 2008 -Question 4

May 10, 2008
combinatorics proposedcombinatorics

Problem Statement

How many sequences a1,a2,...,a2008 a_1,a_2,...,a{}_2{}_0{}_0{}_8 are there such that each of the numbers 1,2,...,2008 1,2,...,2008 occurs once in the sequence, and i∈(a1,a2,...,ai) i \in (a_1,a_2,...,a_i) for each i i such that 2≤i≤2008 2\le i \le2008?
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