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I made a rock paper scissors game and a dice rolling simulator as my first projects - they were pretty easy to code and good starters
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you can pretty much do everything other languages do . Python is a very powerful language and it is used a lot , there is "almost everywhere"
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I personally think a good intermediate program would be a solitaire type game, or poker, like Texas holdem. I feel it incorporates a lot of math functions and object oriented principals that should help hone your skills.
It also allows you to go through a discovery process that most projects require to gather what the program has to actually do, before even beginning the first line of code.