Question:
Consider a board covered by square tiles(like a chess set only of a size of your choosing) and colored like a chess set. Two "people" are placed in different areas of the board and randomly wander around until they "find each other" meaning the two overlap on the board.
A person can move up, down, left, or right for every turn with the same probability unless he is at the edge of the board in which case his movement is limited to three or only two options(if cornered)
Determine the average time it takes for the two to meet (their initial placements also being random yet the placements cannot be of a different color so as to avoid the case in which they never meet)
I am only expecting you to give your thoughts given this is a tough combinatorics problem
My work:
I haven't looked at this problem with a mathematical approach but rather I wrote a Python algorithm to simulate such an experiment. If someone is interested in the code you can find it here: https://github.com/byb263/stock_info/blob/master/feefreer