The Game of Number Guess – the Decimal Version


The game is a simple number-guessing game: students try to guess a “mystery number” and are given clues as to whether their guesses are too high or too low. Students who win get to pick the next number. Winning means you must give the clues to the class, and giving the too-high or too-low clues can be a challenge for many students. It turns that you can guess the number within a certain number of guesses if you guess optimally. In fact, you can always guess a number between 1 and 10 within 5 moves. (Try it.)

The assumption of this game is that the mystery number will be a whole number. But what if 4 is too big and 3 is to small? What would be your next guess? If you guess 3.5 that’s too big.

One way to look at the problem is to think of the numbers living on a line from 2 to 6.

Notice that the next guess should be between 3 and 3.5.