Dozens

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.

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.