Are static fields inherited?

When static members are inherited, are they static for the entire hierarchy, or just that class, i.e.:

class SomeClass
{
public:
    SomeClass(){total++;}
    static int total;
};

class SomeDerivedClass: public SomeClass
{
public:
    SomeDerivedClass(){total++;}
};

int main()
{
    SomeClass A;
    SomeClass B;
    SomeDerivedClass C;
    return 0;
}

would total be 3 in all three instances, or would it be 2 for SomeClass and 1 for SomeDerivedClass?

The answer is actually four in all cases, since the construction of SomeDerivedClass will cause the total to be incremented twice.

Here is a complete program (which I used to verify my answer):

#include <iostream>
#include <string>

using namespace std;

class SomeClass
{
    public:
        SomeClass() {total++;}
        static int total;
        void Print(string n) { cout << n << ".total = " << total << endl; }
};

int SomeClass::total = 0;

class SomeDerivedClass: public SomeClass
{
    public:
        SomeDerivedClass() {total++;}
};

int main(int argc, char ** argv)
{
    SomeClass A;
    SomeClass B;
    SomeDerivedClass C;
    
    A.Print("A");
    B.Print("B");
    C.Print("C");
    
    return 0;
}

And the results:

A.total = 4
B.total = 4
C.total = 4

3 in all cases, since the static int total inherited by SomeDerivedClass is exactly the one in SomeClass, not a distinct variable.

Edit: actually 4 in all cases, as @ejames spotted and pointed out in his answer, which see.

Edit: the code in the second question is missing the int in both cases, but adding it makes it OK, i.e.:

class A
{
public:
    static int MaxHP;
};
int A::MaxHP = 23;

class Cat: A
{
public:
    static const int MaxHP = 100;
};

works fine and with different values for A::MaxHP and Cat::MaxHP -- in this case the subclass is "not inheriting" the static from the base class, since, so to speak, it's "hiding" it with its own homonymous one.

It is 4 because when the derived object is created, the derived class constructor calls the base class constructor.
So the value of the static variable is incremented twice.

#include<iostream>
using namespace std;

class A
{
public:
    A(){total++; cout << "A() total = "<< total << endl;}
    static int total;
};

int A::total = 0;

class B: public A
{
public:
    B(){total++; cout << "B() total = " << total << endl;}
};

int main()
{
    A a1;
    A a2;
    B b1;

    return 0;
}

It would be:

A() total = 1
A() total = 2
A() total = 3
B() total = 4

SomeClass() constructor is being called automatically when SomeDerivedClass() is called, this is a C++ rule. That's why the total is incremented once per each SomeClass object, and then twice for SomeDerivedClass object. 2x1+2=4

3 in all three instances.

And for your other question, it looks like you really just need a const variable instead of static. It may be more self-explanatory to provider a virtual function that returns the variable you need which is overridden in derived classes.

Unless this code is called in a critical path where performance is necessary, always opt for the more intuitive code.

Yes, the derived class would contain the same static variable, i.e. - they would all contain 3 for total (assuming that total was initialized to 0 somewhere).