Sure, here are the answers to your fill-in-the-blank questions based on the terms you've provided:
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A government ruled by a few powerful people
Answer: Oligarchy -
In ancient Greece, an athletic competition held every four years in honor of Zeus
Answer: Olympic Games -
Conflict between Athens and Sparta
Answer: Peloponnesian War
For "rich landowners," the term you are looking for is likely aristocrats.
If you need further assistance, feel free to ask!