Here’s an easy game to try with a friend. All you need is a pen and paper.

### You will need

- A person to play with
- Piece of paper and a pen (optional)

### What to do

There are two roles in this game. You will need one person to choose a number, and the other to guess it.

- The chooser picks a secret number between 1 and 100, and then tells the guesser to start guessing.
- The guesser should guess one number and say it out aloud.
- If the guess was too high, the chooser should say ‘too high’.
- If the guess was too low, the chooser should say ‘too low’.
- The guesser keeps making guesses and getting replies until they guess right.
- Keep a count of the number of guesses it took to get to the secret number. Swap roles in the game, so the old guesser becomes the new chooser, and have another go.
- Try playing with numbers between 1 and 1000 or -100 and 100, or even try with no limits on the number.

### What’s happening?

Trying to guess a number between 1 and 100 with no clues is very hard. You would probably need a lot of guesses because there’s no way to know what the answer is. In this activity, you get a clue each time you make a guess and that makes the game a lot shorter (and more fun)!

This game is an example of an iterative process. You start by making a guess, and you get some information back about your guess. You then use that information to make a better guess.

Iterative processes are important in mathematics, but non-mathematicians also use them. For example, carpenters will cut a piece of wood almost to the right size, check how close they are, and then sand it down to fit perfectly. Of course, when you’re cutting wood, it’s always important to cut it a bit too long, because you can’t stick more wood on the end if you cut it too short!

### Applications

A stable iterative process will keep getting closer to the right answer, but some of them get there faster than others. If you started guessing with 1, 2, 3 … when the answer was 87, then you’d get there eventually, but starting at 50 will get you there faster.

One of the best ways of playing ‘guess my number’ is by using a binary search. First, you need to work out the range of numbers that could be the answer – at the start of the game, the number is between 1 and 100. Then, make a guess that’s in the middle of the range – so your first guess would be 50. If it’s higher, your next guess will be the middle of 50 and 100 – so, 75 – and so on. This method will halve the range of numbers every time you use it, so you eliminate a lot of wrong answers very quickly. Using this strategy, you should be able to guess any number from 1 to 100 in only seven guesses!

### More information

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