## Cyclic Numbers

Consider the number 2387. We can construct new numbers from the same digits by moving them cyclically:

3872, 8723, and 7238.

in general, we can construct n cyclic numbers from a number containing n digits:

.

What is the sum of all the cyclic numbers of such a set ? it is easy to compute this from the above description. When we add all the numbers above, we find that in each vertical column, the sum simply is

so that if we factor it out, the remaining factor will be , with the number repeated n times. In our example, chosen above, we should get

.

You can verify that this is indeed true.

There are several puzzles related to cyclic numbers. You are most welcome to share with us.

-Nalin Pithwa

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