Put these in order by moving the fewest names:

Washington, Wilson, Johnson, Johnson, McKinley, Davis, Jackson, Taft, Kennedy

Moving a name to between two other names, before the first name, or after the last name all count as one move. Thus, exchanging #2 and #7 requires two moves (since you'd have to move #2 and then move #7).

Note that "order" need not necessarily mean chronological order.

UPDATE: So far, no right answers ("right" = "the one I think is cool") in the first 11 posts, so I suppose this is a tough one. If you like this, please forward it to puzzle-loving friends (or discussion lists).

FURTHER UPDATE: Ed Johnson, in the comments, got it; Bob W almost got it.

TMA (mail):
well, if you don't specify the property with respect to which to order them, I'd say they're in order already.
9.8.2005 12:42pm
Patrick McKenzie (mail):
Spoken like a true engineer. The order he means is probably an interesting order, not, for example, "Order under a hashing function constructed specifically to produce this same order".
9.8.2005 12:58pm
DNL (mail):
1) Move McKinley to the end.
2) Move Jackson to the beginning.
3) Move Washington after the second Johnson (and therefore now before Taft).

They are now in order (I think). What order? Alphabetically, if you spell their names backward.
9.8.2005 1:21pm
Joshua Hosseinof:
Move Davis to the beginning, so you end up with a list ordered by people who were not U.S. Presidents, and then those who were U.S. Presidents. Unless you consider the confederacy part of the U.S.
9.8.2005 1:22pm
Jared (guest):
It would take five moves to put them in order by the length of their surname, shortest to longest.

It would take four moves to order them by length of given name in the same manner.
9.8.2005 1:24pm
Kevin Murphy (mail) (www):
Three moves to get:

Jackson, Wilson, Johnson, Johnson, Washington, Davis, Taft, Kennedy, McKinley

which is alphabetical by inverse order of letters in name. NOSKCAJ being first.

Is this silly? Certainly.
9.8.2005 1:24pm
Paul Rosenzweig (mail):
Move "Davis, Jackson" as a single unit before the first "Johnson" [OK -- you can count that as two moves if you like.] Then move "Kennedy" after the second Johnson, so that we now have: Washington, Wilson, Davis, Jackson, Johnson, Johnson, Kennedy, McKinley, Taft.

If you consider that the list is modular, and resumes at the front end after the conclusion, the list is now in alphabetical order, begining with Davis and moving forward and around to end with Wilson.

I'm sure this is not the answer we are looking for -- but in just two [OK maybe 3] moves I get an alphabetical list ...
9.8.2005 1:25pm
Perhaps it is not Jefferson Davis, but Geena Davis.
9.8.2005 1:26pm
Kevin Murphy (mail) (www):
Hmmm DNL beat me to it, but he's slightly off in his explanation, foregtting about Davis.
9.8.2005 1:26pm
DNL (mail):
Kevin, I think I beat you to it. Silly minds do indeed think alike, though.
9.8.2005 1:27pm
Mike Z (mail) (www):
The real question is, what is the order? Obviously, not chronological. Next is party. Alphabetical doesn't seem likely - too many moves. The "Johnson, Johnson" pair is intriguing, because we can reverse the pair without moving at all - just think the first names.

Like many similar problems, it's likely that more than one "order" will emerge.

Wait a minute! Davis???

Consider the following curve-ball: the full names are Harold Washington (College in Chicago), Mount Wilson, Howard Johnson, ...
9.8.2005 1:27pm
Kevin Murphy (mail) (www):
perhaps these are counties in some state somewhere. Or cities by population? Or frequency of occurance of last name?
9.8.2005 1:30pm
Kevin Murphy (mail) (www):
DNL, yes, but I beat you to pointing out that you beat me to it!
9.8.2005 1:30pm
One move:

Put Jackson at the front of the list, and they're in (descending) order of age at election to president.
9.8.2005 1:41pm
random (mail):
Make no moves.

The ordering is the ascii code of the second letter from the right of the name as read from left to right encrypted by a DES64 algorithm with a key which I will release to you once you acknowledge the correctness of this answer.
9.8.2005 1:49pm
Bob W (mail):
Two moves:
Put Washington between the Johnsons.
Move Jackson after Taft.

And get away from the Executive Branch.
9.8.2005 1:53pm
Henry Woodbury (mail):
Why just one Jackson?
9.8.2005 2:03pm
Steve Donohue (mail) (www):
Damn you, Bob W! I thought I had it first!

Hmmm...Bushrod Washington. You learn something new everyday.
9.8.2005 2:05pm
Steve Donohue (mail) (www):
Because there was only one Jackson president- so it throws you off. Besides, regardless of which justice you choose, it's still the same chronology.
9.8.2005 2:06pm
Jeff R.:
Swap one of the Johnsons with Jackson.

You're then in alphabetical order by middle name, with the people who had no middle name in arbitrary order.
9.8.2005 2:14pm

Jackson after Washington
Taft after Washington
Kennedy after Wilson
McKinley before the 2nd Johnson

You get:

Washington, Jackson, Taft, Wilson, Kennedy, Johnson, Johnson, Davis

Which is the order, decending, of how many USSC justices were named by each man

8, 5, 5, 3, 2, 2, 1, 0, 0
9.8.2005 2:27pm
Jeffrey King (mail) (www):
Assume Davis = Gina Davis.

Move Davis to end of the list (three moves)

The list is now in decending alphetibical order of profession:

President, President, President, President, President, President, President, President, Actor
9.8.2005 2:32pm
Shelby (mail):
If you treat Davis as a President based on his position in the Confederacy, 4 moves to get chronological order:
Jackson after Washington
Davis after Jackson
Johnson after Kennedy
Wilson after Taft

If you want date of first election to federal office, do your own research. I also considered highest military rank attained, but Wilson (at least) doesn't seem to have served.
9.8.2005 3:03pm
W J J Hoge (mail):
Mt McKinley (Alaska) 20320 ft
Mt Wilson (Colorado) 14246 ft
Mt Kennedy (Yukon) 13904 ft
Mt Johnson (Calif) 12871 ft
Mt Johnson (Wash) 7680 ft
Mt Washington (NH) 6280 ft
Mt Taft (VT) 4393 ft
Mt Jackson (NH) 4052 ft
Mt Davis (NH) 3213 ft

Move McKinley to first position.
Move Kennedy between Wilson and Johnson.
Swap Jackson and Taft.
Move Davis to last position.
Move Washington between Johnson and Taft.
9.8.2005 3:04pm
W J J Hoge (mail):
Opps, a typo!
Mt Davis is in PA.
9.8.2005 3:06pm
ed johnson (mail) (www):
One move: put Washington between the two Johnsons.

9.8.2005 3:34pm
Blar (mail) (www):
Three moves to get Jackson, Wilson, Washington, Johnson, McKinley, Davis, Taft, Johnson, Kennedy, nine presidents ordered by decreasing length of their term in office (with one tie between Jackson and Wilson). Moves are: Wilson and Jackson to front, Johnson down to come between Taft and Keneddy.
9.8.2005 3:54pm
Blar (mail) (www):
Lengths of term in office to nearest month: years, months

8, 0 Jackson
8, 0 Wilson
7,10 Washington
5, 2 Johnson (LB)
4, 6 McKinley
4, 3 Davis
4, 0 Taft
3,11 Johnson (A)
2,10 Kennedy
9.8.2005 4:11pm
Warmongering Lunatic:
Well, i'm certain this is wrong, but . . .

Move Davis after Washington, Wilson after Johnson, and McKinley after Taft.

Electoral Vote Percentage:
Washington -- 100% in 2 elections
Davis -- 100%
Johnson (A) -- 91% (as VP, 1864)
Johnson (LB) -- 90% (1964)
Jackson -- 82% (1832)
Taft -- 66%
McKinlesy -- 65%
Kennedy -- 58%
9.8.2005 4:18pm
random (mail):

The problem with that is that there are two Jacksons and one Johnson, not two Johnson and one Jackson.

Soooo, is this a typo here? (Because otherwise it would make sense).
9.8.2005 5:18pm
random (mail):
My Bad, you are right (two Johnsons and no need to worry about which Jackson).
9.8.2005 5:22pm
42USC1983 (mail):
Five moves gives you their names in alphabetical order.
9.8.2005 5:48pm
Angus Dwyer (mail) (www):
If you move Washington into the #3 position (between the two Johnsons) and leave everything else as it is, you have them in chronological order of appointment to the Supreme Court.

1. (James) Wilson, app. 10/5/1789
2. (Thomas) Johnson, app. 8/6/1792
3. (Bushrod) Washington, app. 2/4/1799
4. (William) Johnson, app. 5/7/1804
5. (John) McKinley, app. 1/9/1838
6. (David) Davis, app. 12/10/1862
7. (Howell) Jackson, app. 3/4/1893
8. (William Howard) Taft, app. 7/11/1921
9. (Anthony) Kennedy, app. 2/18/1988
9.8.2005 6:44pm
Eugene Volokh (www):
Ed Johnson is right; Bob W was almost right.
9.8.2005 6:46pm
William Baude (mail) (www):
It is not strictly an answer to the question any more, but I cannot help but append this quote from David Currie's empirical investigation of "insignificant" justices.

The secret of a good questionnaire is to be sneaky. There must be Justices everyone remembers, like John Marshall; there must be names of people one is likely to think might or should have been [*479] Justices, like Learned Hand and Daniel Webster; there must be people whose names are easily confused with those of actual Justices, like Edward Livingston, Caleb Cushing, and John Chipman Gray; there should be a misleading plethora of people named Johnson (Andrew, Michael, Thomas, William, and Pearl). Most important of all, there should be a substantial number of people (real or imaginary) who, like Wayne Terwilliger and Emil Verban, have achieved a substantial measure of anonymity in other pastures. In such carefully controlled surroundings, I submit, Justices like Howell Jackson, John Blair, and Samuel Blatchford may find a true test of their own obscurity.

David Currie, The Most Insignificant Justice: A Preliminary Inquiry, 50 U. Chi. L. Rev. 466 (1983).
9.8.2005 10:14pm