433. A certain rectangle is divided by lines parallel to its sides into squares with a side of 1, which are painted in a checkerboard pattern in white and black. The diagonal of the rectangle has broken into white and black segments. Find the ratio of the sum of the lengths of the white segments to the sum of the lengths of the black segments, if the size of the rectangle is a) $100 \times 99$; b) $101 \times 99$.
433. Answer: a) 1; b) $5000 / 4999$.

a) under symmetry relative to the center of the rectangle, the coloring transitions to the opposite.

b) it is necessary to consider the projections of the white and black segments onto one of the sides of the rectangle.