What are dunder (magic) methods?

Question presented to candidate: "You keep seeing methods like __init__, __len__ and __add__ with double underscores on both sides. What are these dunder or magic methods, who calls them, and how would you use them to make your own class work with operators and built-ins?"

What a strong answer should cover:

• Dunder ("double underscore") methods are special method names that Python's syntax and built-ins call for you: a + b calls type(a).__add__(a, b), len(x) calls __len__, print(x) calls __str__, with calls __enter__/__exit__.
• They let a user-defined class implement protocols (number, sequence, container, iteration, context manager, callable) so it behaves like a built-in type.
• Binary operators return the NotImplemented singleton when they cannot handle the other operand, so Python tries the reflected method (__radd__) and finally raises TypeError.
• Implicit invocation looks the method up on the type, not on the instance: setting obj.__len__ on an instance does not change len(obj).
• Defining __eq__ without __hash__ sets __hash__ to None, which makes instances unhashable.
• You implement dunders, you rarely call them directly: use len(x) not x.__len__(); and you do not invent new __names__ of your own.

Code / implementation expected: Yes — a small class (a vector, money or a deck) with __repr__, __eq__, an arithmetic operator returning NotImplemented, and a container method such as __len__.