Bettas are hardy and would be quite happy in a small (5 gallon ish) tank. They are relatively cheap (depending on what you consider cheap) like $3. They can live for 5 years, I believe, but of course all animals can outlive the average given proper care and good health.

A smaller tank doesn't give you too many options as far as hardy fish go. Goldfish are another option. They produce more ammonia than the average fish, so one is good. Although I would say a filter would be better for a goldfish.

That's all I can think of at the moment that would be happy in a smaller tank and doesn't need a filter.
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Phishie
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