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I've been playing around with cuisenaire rods, this is what I came to.
There are five different ways for us to make the pink rod using just red and white rods.

 


We count white, white, red as different from the white, red, white even though they both use two white rods and one red rod.

 

Using the interactivity below, can you work out how many different ways there are, using only the red and white rods, to make up:

  • The light green rod?
  • The yellow rod?
  • The dark green rod?
  • The black rod?
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Without using the interactivity, how many different ways are there to make up the orange rod (equivalent to 10 white rods)?

Can you explain the pattern?