Even among a million numbers, 20 guesses are enough
This is a game where you try to guess a hidden number from 1 to n. You get hints telling you only whether your guess is "larger" or "smaller." If you cut the range in exactly half each time, you can find the number in surprisingly few guesses, no matter how large the range is.
Strategy: Always guess the middle of the remaining range. If the hint says "larger," discard the lower half; if it says "smaller," discard the upper half. Because the range is cut in half each time, a number among n possibilities can always be found in log₂(n) guesses.