[zoombini]

The written solution has arrived today. (The Engineer).

Number the balls 1 to 8.
Denote weighings W1, W2, W3.


W1 Put aside balls 7 & 8. Weigh balls 1, 2, 3 against 4, 5, 6.
If they balance, 7 or 8 is light/heavy.

W2 (a) Weigh 7 against any one of 1 to 6: this will show if 7 is heavy, light or the same.

W3 (a) If the same repeat with 8.

If 1, 2,3 is heavier than 4, 5, 6 on the first weighing then 1, 2 or 3 is heavy or 4, 5, or 6 is light.

W2 (b) Weigh 1, 2, 4 against 3, 7, 8.
If 1, 2, 4 are heavy then 1 or 2 is heavy.

W3 (b) Weigh 1 and any ball except 2. Either one will be the heavier, or, if the same, 2 is heavy.

If in W2 (b) 1,2,4 is light then either 4 is light or 3 is heavy.

W3 (c) Weigh 4 against anything but 3. If the same then 3 is heavy.

Hmm, too heavy for me, but I understand it now.