2. The cells of a $100 \times 100$ table are painted white. In one move, it is allowed to select any 99 cells from one row or one column and repaint each of them to the opposite color - from white to black, and from black to white. What is the minimum number of moves required to obtain a table with a checkerboard pattern of cells?
Answer: in 100 moves. Evaluation: to repaint each of the cells on the black diagonal, a move is required. Example: repaint all rows and columns with odd numbers. In this case, in the $k$-th row and $u$-th column, we will not repaint their common cell. It is easy to see that as a result, we will get a chessboard coloring (with a white diagonal of cells of the form $(k, k)$).