Part one   (the easy bitsy, witsy)
- Name all the countries currently competing in the Winter Olympics in
Torino (or Turin)

Part two The Hard bit

If you were to take each country (listed above) and lets say a country
were in the Northern Hempisphere you were to measure the distance of
the country's most Northern point to the equator OR if the country is
in the southern hempisphere you were to measure the distance from the
southern most point of the country to the equator.

So the question is this Having done this calculation for each country
competing in the Winter Olympics what are the FOUR countries where
this distance is LEAST?
  

Many many best of best regards

Mongolia

Dear mongolia-ga,

Hello again.

The official Torino web site appears to have a slight mistake on it.
In one section it states that 84 countries are taking part in the
games and yet their list of countries only contains 80. I have done a
general search on Google and the overwhelming response is that there
are 80 countries taking part. The list appears at the bottom of this
page.

?Over 2,500 athletes coming from 84 different nations will be
competing at the Torino 2006 Olympic Winter Games in 15 different
disciplines.?
http://www.torino2006.org/ENG/OlympicGames/sport_ed_atleti/atleti_squadre.html

Overwhelming Google hits show 80 counties. 
://www.google.co.uk/search?q=torino+%2280+countries%22&hl=en&lr=&start=10&sa=N
torino "84 countries"
://www.google.co.uk/search?hl=en&q=torino+%2284+countries%22&btnG=Search&meta=

Having found the list, I then used this web site which utilises Google
Maps to find the country and then used the red pointer to plot the
latitude of the various countries. The figures may seem precise but in
fact they are not exact as I could not zoom in enough to precisely
place the marker on the country?s border, but it is enough for your
purposes as there are no close ties.
http://www.mapbuilder.net/

And the winners are:

Kenya is astride the equator.
From North: 4.631179340411012
To South: -4.740675384778361

Brazil is also astride the equator but extends a long way south so it
may be eliminated depending on how you want to treat countries astride
the equator.
From North: 5.178482088522876
To South: -33.79740876757248

Costa Rica
North: 11.221510260010541

Venezuela
North: 12.205811257828273

Ethiopia
North: 14.859850400601037

Senegal
North: 16.688816956180833


If you want to find out the names of the competitors from these
countries, use the first link in this answer and search by continent.

I hope this answers your question. If it does not, or the answer is
unclear, then please ask for clarification of this research before
rating the answer. I shall respond to the clarification request as
soon as I receive it.
Thank you
answerfinder



Africa - 6
=====
Algeria  	
Ethiopia  
Kenya  	
Madagascar  
South Africa  	
Senegal  

Asia - 16
====
People's Republic of China	
Hong Kong, China
India  
Islamic Republic of Iran
Japan  
Kazakhstan
Kyrgyzstan  
Republic of Korea
Lebanon  
Mongolia
Nepal  
Democratic People's Republic of Korea
Thailand  
Tajikistan
Chinese Taipei	
Uzbekistan

Americas - 9
=======
Argentina	
Bermuda
Brazil	
Canada
Chile	
Costa Rica
Virgin Islands	
United States of America
Venezuela	

Europe - 47
=====
Albania  	
Andorra  
Armenia    
Austria
Azerbaijan  
Belgium
Bosnia and Herzegovina	
Belarus
Bulgaria	
Croatia
Cyprus	
Czech Republic
Denmark  
Spain
Estonia	
Finland
France	
Great Britain
Georgia	
Germany
Greece	
Hungary
Ireland	
Iceland
Israel	
Italy
Latvia	
Liechtenstein
Lithuania  
Luxembourg
Republic of Moldova  
Former Yugoslav Republic of Macedonia
Monaco	
Netherlands
Norway	
Poland
Portugal	
Romania
Russian Federation    
Serbia and Montenegro
Slovenia   
San Marino
Switzerland  
Slovakia
Sweden	
Turkey
Ukraine 

Oceania - 2
======
Australia	
New Zealand

Answerfinder 
Many thanks for what has been an absolute spot on answer.It never
really occured to me that countries which actually lie on the equator
would actually be sending atheletes to the winter Olympics
Mongolia

funny, during the opening ceremonies, I also heard the figures 80 and
84 being used interchangeably, depending on who was talking. I think
some people got ehir lists wrong, or maybe some counts are wrong
because of China (Hong Kong and Chinese Taipei/Taiwan), North-South
Korea coming in together, the US Virgin Islands, etc being counted
differently by different people. I haven't actually counted, though,
so this is just an idea.

Dear mongolia-ga,
Thank you for the tip. I enjoyed researching your question.
answerfinder-ga