coreutils: Conditional Executability

 
 27.2.4 Conditional Executability
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 There is one more special type of symbolic permission: if you use ‘X’
 instead of ‘x’, execute/search permission is affected only if the file
 is a directory or already had execute permission.
 
    For example, this mode:
 
      a+X
 
 gives all users permission to search directories, or to execute files if
 anyone could execute them before.