Can a Static method access a private method of the same class?

Question

I have this question because of the singleton/named constructor. In both cases, the real constructors are protected or private, neither of which can be accessed from outside

Answer 1

According to the standard §11/p2 Member access control [class.access] (Emphasis Mine):

A member of a class can also access all the names to which the class has access. A local class of a member function may access the same names that the member function itself may access.¹¹³

_{113) Access permissions are thus transitive and cumulative to nested and local classes}.

Since a static member function is a member of a class it has access to all the names to which the class has access and consequently to the constructor of the class itself.

Consequently, in your example:

class A {
  A(int x);  
public:
  static A createA() { return A(0); } // named constructor  
};

static member function A::createA() has access to call private constructor A::A(int).