Number Guessing

Mathematical Principles & Theorems

Demonstrates the logarithmic efficiency of the Binary Search algorithm. For an ordered search interval of size \(N\), each optimal midpoint comparison \(M = \lfloor(L+R)/2 floor\) eliminates half the candidate values. Time complexity is \(\mathcal{O}(\log_2 N)\). The information-theoretic lower bound guarantees that any number in \([1, N]\) can be determined in at most \(\lceil \log_2 N ceil\) guesses (e.g., \(\lceil \log_2 100 ceil = 7\) attempts).

Operating Instructions

• Select difficulty level: Easy (1–50), Medium (1–100), or Hard (1–200).
• Enter your numerical guess in the input box and click 'Check My Guess'.
• Follow the high / low guidance to bisect the remaining search interval optimally.
• Track total attempts to verify theoretical logarithmic convergence \(\log_2 N\).