If the teacher or students have unexcused absences, the principal questions
which pronoun correctly completes the sentence?
them
him
us
her

Them

When trying to determine what pronoun to correctly use in a sentence, one must always refer back to its antecedent or antecedents.  If the antecedent is singular, then the pronoun should, too, be singular.  If the antecedent if plural, then the pronoun, too, be plural.  Or, if the subject is a compound subject, the pronoun should be plural, as well.  Thus, when we look at the antecedents you have provided, we see that they are plural because there are two, and we will need a plural pronoun.  Additionally, the plural pronoun should be in the third person because the narrator/speaker does not seem to be including him/herself in the subject and is speaking about the teacher and students.  

different routes can lead to sammy to different places, with different roads.   if you check a map, you can see the routes.   try to make connections of the places and count how many there are.   hope this : )