What is the difference between void, undefined and never as return types?

Question presented to candidate: "When you write a function's return type, what is the difference between void, undefined and never? When would you pick each one, and why can a callback typed () => void return a number?"

What a strong answer should cover:

• void means "the caller should not use the result"; undefined means "the caller gets exactly the value undefined"; never means "this function never returns normally" (it always throws or loops forever)
• Assignability: never is assignable to everything, undefined is assignable to void, but void is not assignable to undefined, and nothing except never is assignable to never
• The void function-type rule: a callback type (x) => void accepts a function that returns a value (that is why arr.forEach(x => list.push(x)) compiles), while a declaration annotated : void may not return a value
• Inference: no return gives void; a function declaration that only throws is still void, but a function expression or arrow that only throws is never; TypeScript 5.1 lets a : undefined function omit the return
• never in control flow: after calling an explicitly annotated never function, the code is unreachable, so variables are narrowed (the basis of fail() and exhaustiveness helpers)

Code / implementation expected: Yes — three small functions with each return type, plus a callback example showing the void substitutability rule.