What is the minimum number of guesses required?

The theoretical minimum is ⌈log₂ n⌉ where n is the size of the range. For 1–100 this is 7 guesses; for 1–1000 it is 10. This is achieved by the binary search algorithm, which always guesses the midpoint of the remaining range.

How does binary search find the number optimally?

Binary search always guesses the middle value of the current remaining range. Each guess eliminates exactly half of the remaining possibilities regardless of the answer, guaranteeing the minimum worst-case number of guesses.

What is Reverse Mode?

In Reverse Mode you think of a number within the chosen range and the computer tries to guess it using binary search. You respond Higher, Lower, or Correct to each guess. It demonstrates that an algorithm with no prior knowledge can still solve the problem optimally.

Are the numbers truly random?

Yes — the secret number is generated using Math.random() seeded at game start. Each new game picks a fresh random number uniformly distributed over the selected range.

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Number Guessing Game

Classic guess-the-number game with hints, optimal binary search analysis, and a reverse mode where the computer guesses your number.

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About this tool

Play the classic number guessing game with a twist — after you solve it, the game shows the binary search strategy that would have found the number in the minimum possible guesses. Choose Easy (1–50), Medium (1–100), or Hard (1–1000) difficulty, or set a fully custom range. The computer picks a secret random number; you guess and receive 'too high' or 'too low' feedback until you find it. A visual history list tracks every guess and narrows the displayed range in real time. The info panel always shows how many guesses you've used and the theoretical minimum (⌈log₂ n⌉). After solving, an animated walkthrough demonstrates the optimal binary search path step by step. In Reverse Mode, you think of a number and the computer guesses it using binary search — you only reply Higher, Lower, or Correct. Perfect for understanding algorithmic thinking and search complexity.

How to use

1 Choose a difficulty (Easy, Medium, Hard) or set a custom min/max range.
2 Type your guess in the input field and press Enter or click Guess.
3 Read the 'Too High' or 'Too Low' hint and use the narrowing range display to plan your next guess.
4 Continue guessing until you find the number — your guess count is tracked throughout.
5 After solving, click 'Show Optimal Strategy' to see the binary search walkthrough.
6 Try Reverse Mode: think of a number and let the computer find it using binary search.

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