PROBLEM 266

You have a list of names which you wish to alphabetize.  The names are in a list, initially in random order.  The list initially contains one blank line at the top. You can rearrange the names using the following moves:

1) You can move any name on the list to the blank line on the list.  
2)  You can move any alphabetized sequence of names up or down one line on the list, as long as there is room to do so. 

For example, you can move the names as follows:

_DABC → AD_BC → A_DBC → ABD_C → AB_DC → ABCD, 

or another example

CDAB_ → CD_AB →_CDAB →ACD_B → A_CDB → ABCD_

What is the fewest number of moves that will guarantee that any list of ten names can be alphabetized using these types of moves? 

(You can test yourself by entering a list of names (or numbers) on a spreadsheet and adding one blank line on the top.  The moves correspond to moving a single line of the spreadsheet to the blank line, or shifting a block of already ordered names.)

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ã2007 Alberto L. Delgado