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2015 China South East MO Grade 11 P6

Source: 2015 China South East MO Grade 11 P6

January 16, 2018
combinatorics

Problem Statement

Given a positive integer n≥2n\geq 2. Let A={(a,b)∣a,b∈{1,2,…,n}}A=\{ (a,b)\mid a,b\in \{ 1,2,…,n\} \} be the set of points in Cartesian coordinate plane. How many ways to colour points in AA, each by one of three fixed colour, such that, for any a,b∈{1,2,…,n−1}a,b\in \{ 1,2,…,n-1\}, if (a,b)(a,b) and (a+1,b)(a+1,b) have same colour, then (a,b+1)(a,b+1) and (a+1,b+1)(a+1,b+1) also have same colour.
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