One Step Two Steps

A staircase has 12 steps. You can go down the steps one at a time or two at time.

For example:

You could go down 1 step, then 1 step, then 2 steps, then 2, 2, 1, 1, 1, 1 as in the picture.

In how many different ways can you go down the 12 steps, taking one or two steps at a time?

[Hint: Try to do the question for a smaller number of steps and see if you can find a pattern. How many ways can you go down 3 steps? What about 4 steps? What about 5 steps …? ]

Click here for the ONE STEP TWO STEPS worksheet

Click here for the AIMSSEC poster

Click here for the ONE STEP TWO STEPS Inclusion and Home Learning Guide.

Click here for the Notes for Teachers.

This problem is adapted from the NRICH task by the same name with permission of the University of Cambridge. All rights reserved.