When you play the ‘Secret Santa’, you are expected to buy a gift for whoever you are assigned, without letting them know that you are the one buying the gift.

"Whoever" and "whomever" are both relative pronouns, but they have distinct uses. "Whoever" is a subject pronoun, referring to the subject of a verb, while "whomever" is an object pronoun, referring to the object of a verb or preposition. 

In the given sentence, we examine the phrase "...buy a gift for _____ you are assigned."

“You” is the subject of the clause. “are assigned” is the passive verb. And the blank (relative pronoun) is the object — the one you are assigned.

So you're assigned to someone, and that someone is the object of the verb “assign” (even though it’s in passive voice). In this clause, the subject is you, and the relative pronoun is the object.

The correct phrase is therefore “…buy a gift for whomever you are assigned.”

The other option whom lacks a clear relative clause structure to be grammatically correct. Hence, option B is the correct answer .