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'Factor Lines' printed from http://nrich.maths.org/

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Arrange the four number cards (1, 2, 3 and 21) on the grid above to make a diagonal, vertical or horizontal line.
You can put a number card on a square with
  • the same number
  • a multiple of that number
  • a factor of that number.

In how many different ways can you do it?

You can use the interactivity above orĀ this sheet. The interactivity keeps track of the number of different lines you have created and you can view the lines you've already made by clicking 'Show lines'.

This problem has been adapted from the book "Cards on the Table" by Fran Mosley, published by BEAM Education .