There are 5 slots(1,2,3,4,5) and 5 people(A,B,C,D,E). Each of them provide their preferences. A=1, B=2, C=3, D=4, C=4. Given an arbitary starting sequence say BCDEA, going clock wise: how many passes does it take to fill in those slots so that max number of people are happy. People are happy if A gets 1, B gets 2, C gets 3, etc. Remember D and E cannot be kept happy together at the same time because both of them prefer Slot-4.
So Question is : Can you do better than N passes?