Probably everyone has played the "guess my number" game. I choose a target number in some pre-determined range, you try to guess it, and I tell you if you're too high, too low, or if you happened to be lucky and guess it exactly. As most people know, the best strategy for this game is to guess the middle number in the range. If you're right, the game is over in a hurry. But if not, at least you've narrowed the field down to half the original size. You can then make your next guess the middle number of the remaining set of choices.

Now suppose that the target number is chosen randomly from the numbers 1 to 127. (This simply means that each of the 127 possibilities has the same likihood of being the target number.) What is the average number of guesses the usual strategy will require to find the target?

Happy guessing!