Is it possible for Google (or the people at Google) to calculate a
finite number of possible "Google Wacking" searches that result in
only one web site?  (For the rules of Google Wacking see 
http://www.unblinking.com/heh/googlewhack.htm)

In other words, given the content of all the webpages that Google can
search, is it possible to determine how many search requests will
yield only one site as a result?

If my question isn't clear, please comment and I'll try to explain my
question better.

Yes it should be possible for the people at google.  It will not be
possible for people outside of google, low level access to the
datastore would be required.

Really large-scale data-stores such as google use an indexing
technique called hashing.  The search term or key is converted into a
hash number using a hashing algorithm.  The hash number represent a
bucket number (address) within the data-store, where the data is
found.

 It should be possible for google to achieve the wacking in two ways:

1) When a new term hits a new empty address, google could add the term
to a list of wacks.
2) The data store could be searched for buckets containing only one
data item.

I would speculate that answering this problem requires computation of
an NP complete problem. That is, one that cannot be decided in
polynomial time by a deterministic Turing machine, and which is
reducible to another known problem in the NP domain.

It is of course easily possible to determine SOME whacks, but to
determine all of them would probably take more time than the universe
has left.

Incidentally, if you think this is NOT the case, you are in line for a
million dollars, if you can prove it. Have a look at:
http://www.claymath.org/prizeproblems/pvsnp.htm

The two comments above are so good that I don't really need an
"official" answer anymore.

A "Google Whack" is defined as a combination of search terms that
yield exactly one webpage as a search result.

Google can perform about 100,000,000 searches in one day. Google
allows 1,000 searches per external visitor per day. From an exhaustive
search approach:

Finding all one-word Google Whacks would be possible for Google or
even normal visitors such as yourself. That requires about 250,000
searches. Google can do that in less than a day. If you write a small
program and convince seven friends to run it you'll be successful in
about a month.

Finding all Google Whacks consisting of exactly two dictionary words,
which the Whack Stack looks for, would take 32,000,000,000 searches.
At 30,000,000 searches per day that would take about three years.
Cracking these is only possible if you're willing to spend a couple
years dedicated to the effort.

Finding all Google Whacks consisting of exactly three dictionary words
is probably beyond current technology for Google or external visitors.

As technology and the 1,000-query limitation of the Google Web API
increases ( ://www.google.com/apis/ ) over time, this may become
much easier to do.

Enjoy! :)

In response to a previous commenter, this problem is not NP-complete. 
Enumeration of all pairs of English language words is quadratic in the
size
of the dictionary and is sufficient to solve the poster's problem.  I
feel certain that access to the data store makes the problem at worst
linear in the size of the dictionary.

The prize mentioned is for solution of the P =? NP problem.  This
question
on Googlewhacking won't help you win the bounty.

Dear, rickbradley-ga I disagree, sure finding all pairs of words in
the english language is linear, but the reason this problem is
NP-complete is because we are dealing with more than just pairs of
words. A google wack can consist of a string of N words. Where N is
[1,sizeof(dictionary)]. Furthermore to obtain this list one would have
to simply try every combo (or maybe permutation, I am not sure if
order matters in google searches) of words in the dictionary to see if
it results in a "wack". Which is what a NP-complete problem really is
when you boil it down: a problem that only has a bruteforce solution,
which can be solved in polynomial time. AND If someone figured out a
way to know all the google wacks without actually tring every possible
string, then they would have solved the N->NP problem.

To add to the already excellent comments:

Hasn't this already been done to some extent using the Google APIs? 
I've seen some pretty wacky programs written up, and while I don't
remember seeing any calculating a finite number of true Googlewacks it
should be doable.  In theory, at least...

carwfloc-ga

Great application of numbers
to the question but cisco_
specialist, you forgot to mention
the flux in the webpages in the 
database during the three years of
searching that could possibly invalidate
a great deal of searches. ;-)
 
-AI