MathDB
Coloring problem

Source: Indian Postal Coaching 2005

October 27, 2005
combinatorics unsolvedcombinatorics

Problem Statement

Consider the points PP =(0,0)(0,0),QQ = (1,0)(1,0), RR= (2,0)(2,0), SS =(3,0)(3,0) in the xyxy-plane. Let A,B,C,DA,B,C,D be four finite sets of colours(not necessarily distinct nor disjoint). In how many ways can P,Q,RP,Q,R be coloured bu colours in A,B,CA,B,C respectively if adjacent points have to get different colours? In how many ways can P,Q,R,SP,Q,R,S be coloured by colours in A,B,C,DA,B,C,D respectively if adjacent points have to get different colors?
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