Why this is O(1)
Why O(1). Three integer comparisons and a return. There's no loop, no recursion, no size variable in scope — the work is fixed regardless of any input.
The teaching point. O(1) doesn't mean *fast*, it means *the runtime doesn't grow with input size*. A function that does 10,000 fixed operations is still O(1).
How to recognize constant complexity in the wild
O(1) means the runtime doesn't grow with the input at all. Dictionary lookups, array indexing, single-line arithmetic — the input could be ten or ten million and the work is the same.
The eight rungs of the ladder
Big-O classifies the asymptotic growth of a function, not the wall-clock time. The ladder Bugdle uses has eight rungs ordered from cheapest to most ruinous: O(1), O(log n), O(n), O(n log n), O(n²), O(n³), O(2ⁿ), O(n!). The puzzle's answer sits at rung 1 of 8. The four-guess budget plus higher/lower hints means the puzzle is solvable in at most ⌈log₂(8)⌉ = 3 perfectly-read guesses; the fourth attempt absorbs misreads of the snippet.
Common confusables
Nested loops aren't automatically quadratic — the inner loop has to range over n, not a constant. A loop that always runs ten iterations is still O(1) work per outer iteration. Similarly, a recursive function isn't automatically exponential just because it calls itself twice — if the recursion has overlapping subproblems and you memoise, you collapse back to polynomial. Always ask: what does n really mean here, and how many distinct subproblems are there?
External reference: Big O notation — Wikipedia.