In Defense of Reason

I suppose I have to be politically correct...
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Let's say you have four people, a fifteen-year old teenager, an infant, a toddler, and a twenty five-year old man. Now let's say that you are asked to state who the strongest person in this group of four is, based only on the three following conditions.

The teenager is stronger than the toddler.
The toddler is stronger than the infant.
The man is stronger than the infant.

Is it possible to state who the strongest person is? Clearly, the toddler and the infant are the weakest, as they are both dominated by the teenager. But can we differentiate between the man and the teenager? If the man was strongest and the teenager second strongest, the three conditions hold true. If the teenager was the strongest and the man was second strongest, even third strongest, the three conditions still hold true. Therefore, there is not enough evidence show who is the strongest.

Consider the following argument:

The teenager is definitively stronger than two people, the toddler, and the infant. On the other hand, the man is definitively stronger than than one person, the infant only. Because the teenager is stronger than two, whereas the man is only stronger than one, the teenager has to be the strongest.

What kind of logic is this? This is the explanation that my AP Chemistry teacher provided when explaining the solution to this problem. In context, the problem asked us to compare the activity level of four elements, set-up with those conditions.

Now, occasionally, a subject/field can be very frustrating due to a minor topic. For example, memorizing the derivatives and integrals of inverse trigonometry functions in calculus wasn't particularly fun. However, seeing this type of problem-solving in chemistry is downright offensive. It seems that because there is not enough evidence to empirically solve this problem, some bogus explanation that follows no axiom of logic or critical thinking has to be created.

I truly hope that this explanation was simply an abstraction of the truth. I can accept getting a problem wrong, but I can't accept a problem that does not reward sound, empirical reasoning.