Scope and static helpers

Local variables live inside the method that declares them — parameters included. Nothing outside can see them; nothing inside escapes:

public static int twice(int x) {
    int doubled = x * 2;    // local: dies when the method returns
    return doubled;
}

Scope is where a name is visible. A method can read its own parameters and locals; it cannot read another method's. Two methods may each have a local named x — different boxes.

static context: our Solution methods are static, which means they belong to the class, not to an object. A static method can call other static methods of the same class directly by name — that is how helpers compose:

public static int hypotenuseRounded(int a, int b) {
    double c = Math.sqrt(a * a + b * b);
    return (int) (c + 0.5);
}

Math.sqrt is itself just a static method of the Math class — call it as Math.sqrt(x), never new Math() (it has no public constructor).

Pass-by-value: Java copies arguments. Reassigning a parameter inside the method changes only the copy:

public static void bump(int x) {
    x++;              // the caller's variable is untouched
}