## A Nerd’s Way to Walk Up the Stairs

The last time I talked to John H. Conway, he taught me to walk up the stairs. It’s not that I didn’t know how to do that, but he reminded me that a nerd’s goal in climbing the steps is to establish the number of steps at the end of the flight. Since it is boring to just count the stairs, we’re lucky to have John’s fun system.

His invention is simple. Your steps should be in a cycle: short, long, long. Long in this case means a double step. Thus, you will cover five stairs in one short-long-long cycle. In addition, you should always start the first cycle on the same foot. Suppose you start on the left foot, then after two cycles you are back on the left foot, having covered ten stairs. While you are walking the stairs in this way, it is clear where you are in the cycle. By the end of the staircase, you will know the number of stairs modulo ten. Usually there are not a lot of stairs in a staircase, so you can easily estimate the total if you know the last digit of that number.

I guess I am not a true nerd. I have lived in my apartment for eight years and have never bothered to count the number of steps. That is, until now. Having climbed my staircase using John’s method, I now know that the ominous total is 13. Oh dear.

1. #### Paul:

You could invent extensions for two or more nerds climbing the stairs together. The second person could use a pattern to obtain the number of stairs modulo three, and the third person could go for modulo seven. Then at the top of the stairs, they’d know the number modulo 210, which should enough to know the exact number for most staircases.

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3. #### Felipe Pait:

7 x 2 x (7-1) = 84 steps. My stairs have a different geometry.

4. #### Monday link ramblings | MathBlog:

[…] in a while, and you are no different. Unless of course you are the first grade mathematical genius.A Nerd’s Way to Walk Up the Stairs – Tanya Khovanova has made a short blog post on how to walk up stairs, so you can estimate […]

5. #### David Wilson:

13 stairs is actually quite common for a staircase.