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Number of distinct solutions of x,y,z=a

Source: Moldova TST 2006 Test II problem 4

March 25, 2006
combinatorics proposedcombinatorics

Problem Statement

Let A={1,2,…,n}A=\{1,2,\ldots,n\}. Find the number of unordered triples (X,Y,Z)(X,Y,Z) that satisfy X⋃Y⋃Z=AX\bigcup Y \bigcup Z=A
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