Question

By the time Spanish explorers first encountered them, the Aztecs (have developed, had developed) the calendar.

Short answer

The correct sentence is: By the time Spanish explorers first encountered them, the Aztecs had developed the calendar.

Step-by-step solution

Understand the context

Recognise that the words in brackets are verb tenses and should relate to the time sequence in the sentence. The Spanish explorers' encounter with the Aztecs is a past action, the development of the calendar is an event that happened before this encounter.

Choose the correct tense

In the context of the sentence, and considering the time sequence that has been provided, choose the proper tense. 'Had developed' is in the past perfect tense and indicates an action that was completed before the Spanish explorers' encounter, corresponding correctly to the timeline.