Divisibility

'Use what you know about place value, divisibility and spreadsheets to help you solve this tricky problem' 

Arrange the digits from 1 to 9 in such a way that the the number made by the first digit is divisible by 1, the number made by the first 2 digits is divisible by 2, the number made by the first 3 digits is divisible by 3 and so on up until the 9th digit! This is a seriously tricky problem and you will need all your powers of logic along with your understanding of place value to help you solve this! In this activity you will design a spreadsheet to help you solve the problem. Much of the maths is in the design of the spreadsheet and this might take a while, but hopefully it will be worth it once you have. Then you need to apply some logic to what you know about divisibility to help you get to the solution! Good luck!

Resources

The problem is outlined in the  Divisibility worksheet. This can be used on paper or electronically since you will need access to spreadsheet as well.

Solve with a spreadsheet

The following is a brief screen cast to demonstrate how a spreadsheet can be set up to help solve this problem. Much of the mathematics involved in this task is in the setting up of the spreadsheet.

Description

The following is a brief overview of the activity

  • It is important to start by defining the problem. Examples, like the one in the video at the top if the page, are probably the easiest way.
  • Program a spreadsheet to work out the numbers made by each combination of digits and test the divisibility. An example of this is shown in the video above.
  • Test the spreadsheet to check it is doing everything it should.
  • Considering existing knowledge of divisibility, try re-arranging the digits so that all the divisions give whole numbers and thus solve the problem!
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