Solution to Problem 266

The only complete, correct solution came from A. Teitelman, Israel.

You can always arrange the names with ten moves.  Let's assume the names are 1,2,...,10.  (No, I've never met anyone named anything like this; please humor me.)  Move 1 from its initial position k to position 1.  Next move k to the just vacated position k.  Repeat as needed.  I leave to you the (more difficult) task of proving that the initial listing 10,9,...,2,1 requires ten moves.

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ã2007 Alberto L. Delgado