MathDB
Find the # of functions

Source: Korean Mathematical Olympiad 2014 #6

January 24, 2015
functioncountingderangementinductioncombinatorics proposedcombinatorics

Problem Statement

How many one-to-one functions f:{1,2,⋯ ,9}→{1,2,⋯ ,9}f : \{1, 2, \cdots, 9\} \rightarrow \{1, 2, \cdots, 9\} satisfy (i) and (ii)? (i) f(1)>f(2)f(1)>f(2), f(9)<9f(9)<9. (ii) For each i=3,4,⋯ ,8i=3, 4, \cdots, 8, if f(1),⋯ ,f(i−1)f(1), \cdots, f(i-1) are smaller than f(i)f(i), then f(i+1)f(i+1) is also smaller than f(i)f(i).
Back to ProblemsView on AoPS