Question 50
On a rectangular sheet of paper, several segments were drawn parallel to its sides. These segments divide the sheet into several rectangles (so that there are no parts of drawn segments inside rectangles). Petya wants to draw one of two diagonals in each of these rectangles dividing it into two triangles, and then color all triangles, each triangle either black or white. Determine if Petya can always do this so that no two triangles of the same color have a common boundary segment.