In the High/Low game, you will choose a number between 1–1000. The computer will make guesses such as “I guess that your number is 3” in order to determine your number. You will then respond that incorrect guesses are “too high” or “too low.” In the end, the computer always ends up guessing the correct number, but how many guesses are ideal for this task? How many guesses guarantee a correct guess? The computer claims it can guess correctly using at most ten guesses each time. Think about how this relates to the state space in this scenario—the numbers 1–1000.
Revisit the Binary Search tool from Unit 1. Experiment with the applet to determine if this is true. Write your answer in 2–3 sentences including an explanation of your reasoning.
Once you have written up your response, try to apply the same reasoning yourself. Guess the computer’s number in as few questions as possible by playing Funbrain’s Guess the Number game.