Exercise 3 solution

Python version:

def ground_km(map_cm, scale):
    """Map distance in cm and scale number (e.g. 50000) -> ground distance in km."""
    return map_cm * scale / 100 / 1000

def map_cm_for(ground_km_value, scale):
    """Ground distance in km -> centimetres on the map."""
    return ground_km_value * 1000 * 100 / scale

print(ground_km(8, 25000))    # 2.0
print(ground_km(8, 50000))    # 4.0
print(map_cm_for(3, 50000))   # 6.0
print(map_cm_for(3, 25000))   # 12.0

Spreadsheet formulas (map cm in A1, scale number in B1):
  =A1*B1/100000          gives kilometres
  (km in A2, scale in B1)  =A2*100000/B1   gives centimetres

Check: 8 cm at 1:25,000 = 2 km, 8 cm at 1:50,000 = 4 km, matching the
"4 cm = 1 km" and "2 cm = 1 km" shortcuts.