Brain Game: Angie's Number

Price is Right fans should be familiar with the long-running Clock Game, where players are required to guess the prices of two items within 30 seconds by being told if the actual price is "higher" or "lower" than their guesses. It's maddening to see a contestant who performs badly at the Clock Game, since the strategy isn't too hard to figure out. That's the inspiration behind today's mentalfloss.com Brain Game Free-for-All Friday challenge. Good luck!

You ask Angie to choose a whole number from 1 to 100. Whenever you guess a number, Angie will tell you if the number is "lower" or "higher" than the one you've guessed, until you guess correctly. Given this information:

If you choose numbers in the most thrifty manner, what's the MOST number of guesses you should need to come up with any possible answer?

Here is the ANSWER.

THE ANSWER:

You should be able to guess any number in a maximum of SEVEN guesses.

Your first guess would be 50; your second would be 25 or 75 (depending on whether the answer to your first guess was "lower" or "higher"). By continuing to divide the differences, any number should be obtainable in seven or fewer steps.

Thanks for playing!