Question

Brilli the ant randomly placed a token into a square on a 2×100 chessboard according to a probability distribution P. The token is then moved uniformly at random to one of the horizontally, vertically, or diagonally adjacent squares. The probability that the token is in a particular position after it has been moved also satisfies the distribution P. Let q be the probability that the token is placed into one of the columns of C={5,6,…44} and after being moved is still in one of those columns. The value of q can be expressed as a/b where a and b are coprime positive integers. What is the value of a+b?

Please provide a solution along with the answer