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Mr Gilderdale was using this interactivity with his class:


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He had thought of a number rule and he asked the class to choose numbers to test.

If the number they chose fitted his rule, he put it under 'I like these numbers'. If the number they chose didn't fit his rule, he put it under 'I don't like these numbers'.

Here is a picture of the game after the class had chosen four numbers:

I like 5 and 15. I don't like 18 and 22.

What could Mr Gilderdale's rule be?
If you were in Mr Gilderdale's class, which number would you choose next to test your idea?
How could you find out Mr Gilderdale's rule in the smallest number of guesses?