16. We consider all possible broken lines that follow the sides of the cells and connect the two opposite corners of a square sheet of grid paper measuring $100 \times 100$ by the shortest path. What is the smallest number of such broken lines needed so that their union contains all the vertices of the cells?
77.16. Answer. 101 broken lines. The fact that there are no fewer than 101 broken lines follows from the fact that if we consider all the vertices lying on the diagonal connecting two other opposite vertices of the square (there are 101 of them), then no broken line of the specified type can contain two vertices from this set. An example for 101 broken lines is obvious.