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Find the number of functions

Source: Turkish TST 2012 Problem 1

March 26, 2012
functioninductioncombinatorics proposedcombinatorics

Problem Statement

Let A={1,2,…,2012}, B={1,2,…,19}A=\{1,2,\ldots,2012\}, \: B=\{1,2,\ldots,19\} and SS be the set of all subsets of A.A. Find the number of functions f:S→Bf : S\to B satisfying f(A1∩A2)=min⁡{f(A1),f(A2)}f(A_1\cap A_2)=\min\{f(A_1),f(A_2)\} for all A1,A2∈S.A_1, A_2 \in S.
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