Rods and Rods

Using only the red and white rods, how many different ways are there to make up the other colours of rod?
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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.

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Rods and 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.

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Rods and Rods



Using our Cuisenaire environment, 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?



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?