MathDB

22

Part of 2005 Postal Coaching

Problems(1)

Coloring problem

Source: Indian Postal Coaching 2005

10/27/2005
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?
combinatorics unsolvedcombinatorics