I am facing difficulty in solving this problem.. Anybody can help? The problem is as follows: There is a circular 1D chain of two types of persons (say + and -). for example something like +-+--+---++++-+-+ etc. but this is circular. Now each person jumps with probability, + jumps with 'x' probability and - jumps with 'y' probability at time t. the rules of dynamics of this system are as follows. If a person jumps before its right person, it gains a point and the right person loses that point. If the person jumps before its left person, it loses an point and the left person gains a point. How can this system say (number of + persons) be described as an evolving function of time i.e. +(at time t+1) in terms of +(at time t).