Interview arithmetic is small, exact, and always tied to a decision: how big the state space is, how deep the bound must reach, how many bits an abstraction saves. These drills compute each number twice: once by hand in the prose, once in a runnable calculator that also shows the failing variant, so a wrong input is caught, not averaged away. Work them with a pen first, then read the calculator.
Lesson | After it you can... |
|---|---|
Size a state space, justify a bound, and price FIFO depth, induction k, memory, and counter abstraction. | |
Price cones, lassos, unrolled problems, assumption load, mutation gates, and bound justifications. |
Suggested order: top to bottom. The first lesson sizes the machine and the bound; the second prices the engine's work and the assumptions' cost. Every result is labelled illustrative or tied to a running design.
Because a calculator that cannot fail cannot check: the wrong input must be caught visibly, or the number is decoration rather than evidence.