Powerful numerical tools for everyday use

Number Guessing Game

Strategic guessing with optimal algorithms

VS Computer
Challenge the computer to a number guessing duel. You choose a number, and the computer will guess it using optimal algorithms.
Guess Computer's Number
Try to guess the computer's number while learning optimal guessing strategies. See how you compare to the binary search algorithm.
Two Players
Play against a friend. Take turns choosing numbers and guessing each other's numbers to score points.
Range: 1 to 100 (Possible guesses needed: ~7)
Computer is Guessing Your Number
Think of a number between 1 and 100
Guesses
0
Remaining
10
Computer is thinking
Is your number 50?
Current Search Range
1 100
Guess History
# Guess Range Response
Computer's Algorithm: Binary Search

The computer is using the binary search algorithm, which is the optimal strategy for guessing a number in a range. It always guesses the middle of the current range, eliminating half the remaining numbers with each guess.

Guess the Computer's Number
The computer has chosen a number between 1 and 100
Guesses
0
Remaining
10
Best Possible
7
Enter your guess below
Search Range & Optimal Next Guess
1 50 100

The highlighted position shows the optimal next guess using binary search. This would eliminate the most possibilities.

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Clear
0
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Submit Guess
Your Guess History
# Your Guess Optimal Guess Result
Two Player Mode
Take turns guessing each other's numbers
Player 1's Turn
Player 1
0
Player 2
0
Player 1, choose a number between 1 and 100 for Player 2 to guess
Game History
Round Player Target Guesses Points

How to Play the Number Guessing Game

The Number Guessing Game is a strategic game where players try to guess a hidden number within a specified range. This game demonstrates mathematical concepts like binary search and information theory.

Game Modes:

  • VS Computer: You think of a number, and the computer tries to guess it. The computer uses the binary search algorithm, which is the most efficient guessing strategy.
  • Guess Computer's Number: The computer selects a random number, and you try to guess it. Learn optimal guessing strategies by comparing your guesses to the binary search algorithm.
  • Two Players: Play against a friend. Take turns choosing numbers and guessing each other's numbers. The player who uses fewer guesses scores more points.

Optimal Guessing Strategy:

The most efficient strategy for guessing a number in a range is the binary search algorithm:

  • Always guess the middle of the current possible range
  • This eliminates half of the remaining numbers with each guess
  • For a range of 1 to 100, you should be able to find any number in at most 7 guesses
  • The formula for the maximum number of guesses needed is log₂(range size) rounded up

Mathematical Connection:

This game demonstrates information theory concepts. Each optimal guess provides exactly 1 bit of information, reducing the uncertainty by half. The minimum number of guesses required is related to the binary entropy of the uniform distribution over the range.