Exercise 3 solution (Python)

import math

def slope(interval_m, spacing_mm, scale):
    """Ground distance (m), gradient (%) and angle (degrees) between two contours."""
    ground_m = spacing_mm / 1000 * scale      # mm on paper -> m on the ground
    gradient = interval_m / ground_m * 100    # rise over run, as a percentage
    angle = math.degrees(math.atan(interval_m / ground_m))
    return ground_m, gradient, angle

for args in [(10, 4, 25000), (10, 2, 50000)]:
    d, g, a = slope(*args)
    print(f"{args}: {d:.0f} m, {g:.1f} %, {a:.1f} degrees")

Output:
(10, 4, 25000): 100 m, 10.0 %, 5.7 degrees
(10, 2, 50000): 100 m, 10.0 %, 5.7 degrees

Check by hand:
  4 mm at 1:25,000 = 0.004 m x 25,000 = 100 m
  2 mm at 1:50,000 = 0.002 m x 50,000 = 100 m
  10 m up in 100 m = 10 percent; atan(0.1) = about 5.7 degrees

Both cases are the same slope, because a finer scale needs a wider gap on
paper to show the same ground distance.