Is it possible to buy a livable house with $10,000?

I want a second home, and I have about $10,000 cash. I do not want to take on a mortgage. So with $10,000 in cash, where can I buy a small house, a place where I can get away from big city sometimes? Any suggestions: 1. What state? 2. Rural or city? Thanks. (If you have a house in this price range and livable, let me know too.)

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