. . . . . . . . youngest boy has just started going to school, . . . . . . . . eldest boy is in . . . . . . . . college.

In the first blank, article "the" will be used because article 'the' is used with superlatives.
Similarly, In the second blank, article "the" will be used because article "the" is used with superlatives.
In the third blank, "no article" will be used because the term 'college' doesn't need specification. It just refers to a place where the eldest boy is studying.