Learn Russian: Студенты сами справились с этой сложной задачей. - The students handled this difficult task themselves.

Сами is an emphatic pronoun meaning "by themselves" or "on their own" (without outside help). Себя is a reflexive pronoun used when the action is directed back at the subject (like "they see themselves"). Here, the students didn't handle themselves; they handled the task on their own, so we use сами.

Why is it сами and not само or сам?

The emphatic pronoun has to agree in gender, number, and case with the noun it emphasizes. Since студенты is plural and in the nominative case (it is the subject of the sentence), we need the nominative plural form, which is сами.

Why is the phrase этой сложной задачей in the instrumental case?

The verb справиться (to cope, to handle, to manage) requires the preposition с (with) followed by the instrumental case. So, "handled this task" translates structurally as "coped with this task" (справились с этой сложной задачей).

Could we put сами at the very end of the sentence?

Yes, Russian word order is flexible. Saying Студенты справились с этой сложной задачей сами is completely natural. Putting сами right after студенты simply links the emphasis to the students a bit earlier in the sentence.