This problem puts emphasis on trying to gain as much information as
possible from each weighing, whatever the outcome. So if a weighing
has one outcome which gives you a lot of information, but another
outcome which doesn't give you much new information, it is probably
not going to be a useful way of identifying the odd weight.
This problem can be extended further by asking how many weights can
be sorted in 3 weighings, 4 weighings and more generally n
weighings, when you know one is heavier.
To do this, pupils should first try to spot the pattern, then try
to explain why this works by looking at what proportion of weights
can be discarded at each weighing.
What happens if two of the weights are heavier than the rest? What
is the minimum number of weighings now needed to guarantee being
able to identify the two heavier weights
A more challenging follow-up problem can be found at The
Great Weights Puzzle