How to search and select column names based on values?

Suppose I have a pandas DataFrame like this

    name    col1    col2    col3 
0   AAA     1      0        2 
1   BBB     2      1        2 
2   CCC     0      0        2

I want (a) the names of any columns that contain a value of 2 anywhere in the column (i.e., col1, col3), and (b) the names of any columns that contain only values of 2 (i.e., col3).

I understand how to use DataFrame.any() and DataFrame.all() to select rows in a DataFrame where a value appears in any or all columns, but I'm trying to find COLUMNS where a value appears in (a) any or (b) all rows.

source https://stackoverflow.com/questions/73674735/how-to-search-and-select-column-names-based-on-values

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