Challenge Level

*You may find the article on Divisibility Tests helpful.*

Do you know a quick way to check if a number is a multiple of 2? How about 3, 4, 5..., 12..., 15..., 25...?

To start with, the interactivity below will generate two random digits.

Your task is to find the **largest possible three-digit number** which uses the computer's digits, and one of your own, to make a multiple of 2.

**Can you decribe a strategy that ensures your first 'guess' is always correct?**

Clicking on the purple cog gives you a chance to change the settings.

You can vary the challenge level by changing:

- the multiple
- the number of digits in your target number
- the number of digits provided by the computer.

*To ensure you have some choice, make sure the number of digits provided by the computer is fewer than the number of digits in the target number.*

**Can you describe your strategies that ensure your first 'guess' is always correct for a variety of settings?**

**Something else to think about:**

What is the largest possible five-digit number divisible by 12 that you can make from the digits 1, 3, 4, 5 and one more digit?

*Once you've had a chance to think about this, click below to check.*

Many people think the largest possible five-digit number is 53184, but there are larger ones...

Click here for a poster of this problem.

*We are very grateful to the Heilbronn Institute for Mathematical Research for their generous support for the development of this resource.*