Question 169
Given is an $n \times n$ board, whose all cells are initially white. Khalid the Painter walks around the board and recolors the visited cells according to the following rules. Each *walk* of Khalid starts at the bottom-left corner of the board and continues as follows:
* if he is standing on a white cell, he paints it black and moves one cell up (or walks off the board);
* if he is standing on a black cell, he paints it white and moves one cell to the right (or walks off the board).
Determine the minimum positive integer $s$ with the following property: after *exactly* $s$ walks all the cells of the board will become white again.
* if he is standing on a white cell, he paints it black and moves one cell up (or walks off the board);
* if he is standing on a black cell, he paints it white and moves one cell to the right (or walks off the board).
Determine the minimum positive integer $s$ with the following property: after *exactly* $s$ walks all the cells of the board will become white again.