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Set construction with condition


Dear Mathematica experts,

I have this definition of L which generates a list of 81 elements:

L=Flatten[Outer[StringJoin,{"1","X","2"},{"1","X","2"},{"1","X","2"},{"1","X","2"}]]

How can I modify this definition in order to generate only elements in which there are a maximum of 2 characters "1"?

Thanks!!!!!!!!!!!!!!

PS.: I don't want to filter the entire 81 elements set AFTER the generation. I want to generate it with the desired elements.



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