NRICH: Dozens

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

You may find the article on Divisibility Tests helpful.

The problem is explained below, but you may wish to scroll to the foot of the page to watch a video of the NRICH team presenting the challenge.

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  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?

Here is a video of the NRICH team presenting the challenge. You could just watch the start to check that you understand the problem, or you may like to pause the video and work on the task at various points.

Age 11 to 14 

Math Topics
Multiplication & Division
Middle School, High School
6th Grade, 7th Grade, 8th Grade, 9th Grade
Descriptions of PDFs

Click here for a poster of the problem.

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NRICH (University of Cambridge)

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Online Game
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