Exercise 3 solution (Python)

import math

def split_ref(ref):
    """Return (line_e, tenth_e, line_n, tenth_n) from a six-figure string."""
    if len(ref) != 6 or not ref.isdigit():
        raise ValueError("need exactly six digits")
    easting, northing = ref[:3], ref[3:]
    return easting[:2], int(easting[2]), northing[:2], int(northing[2])

def to_metres(ref):
    """Position in metres from the grid origin, 1 km lines and 100 m tenths."""
    le, te, ln, tn = split_ref(ref)
    return int(le) * 1000 + te * 100, int(ln) * 1000 + tn * 100

def distance_m(ref_a, ref_b):
    ea, na = to_metres(ref_a)
    eb, nb = to_metres(ref_b)
    return math.hypot(eb - ea, nb - na)

print(split_ref("346723"))            # ('34', 6, '72', 3)
print(split_ref("351698"))            # ('35', 1, '69', 8)
print(distance_m("346723", "351698")) # about 2,550 m

Check by hand for the test pair:
  346723 -> easting 34,600 m, northing 72,300 m
  351698 -> easting 35,100 m, northing 69,800 m
  difference: 500 m east, 2,500 m south
  straight line = sqrt(500^2 + 2500^2) = about 2,550 m

The program and the hand check agree: about 2,550 m.