Originally posted by luskin
More interesting is, what do you do if the first weighing does not balance.
if the first weighing (3a v 3b) was unequal, you know the 4 unweighed are genuine.
and you know which of 3a or 3b was heavier (lets say 3a was heavier)
for the second weighing balance 3 genuine against 3a
3g = 3a => 3b contains a light coin
3rd weighing - weigh any 2 of 3b against each other to find the light one
3g < 3a => 3a contains a heavy coin
3rd weighing - weigh any 2 of 3a against each other to find the heavy one
3g > 3a => 3g > 3a > 3b which is not possible