If the question only asked for 41, then the question is WRONG ....
- or at least woefully out of date. When was the question written? If it was before the breakup of the Soviet Union, then it is off by 7. If it was written before the breakup of Yugoslavia, it is off by 6. (Kosovo became an independent country only 17 months ago.) If it was written before Czechoslovakia broke into the Czech Republic and Slovakia it is off by 1.
You asked for the CURRENT countries of Europe - as of 20 July, 2009. You asked in the Geography category, so the answers will be based upon a country's geography alone. It has no relationship with the European Union, or the Schengen Treaty, or the European Broadcasting Union, or the International Federation of Association Football.
You got a very thorough answer - with authoritative sources. Here it is again:
The geographical boundaries of Europe aren't totally agreed upon - not precisely; especially the border in the trans-Caucasus region. As closely as can be measured, by the internationally agreed borders, Azerbaijan, Kazakhstan, and Turkey have portions in Europe as well as Asia. Armenia and Georgia do not; they are in Asia only. (Some disagree with this last; none are geographers) Also, Cyprus, Iceland, and Malta are considered a part of Europe even though they are some distance from the European mainland.
Thus, there are 48 sovereign states in Europe:
7. Bosnia and Herzegovina
11. Czech Republic
20. Republic of Ireland
38. San Marino
47. United Kingdom
48. Vatican City
There are 4 Partially recognised republics, territories and regions. They have partial diplomatic recognition by one or more sovereign states and are defined as 'states' by the declarative theory of statehood. (Number of countries recognizing the country in parentheses)
1. Abkhazia (2)
2. Kosovo (62)
3. Turkish Republic of Northern Cyprus (1)
4. South Osettia (2)
There are 3 unrecognised republics, territories and regions. They lack diplomatic recognition, yet are defined as 'states' by the declarative theory of statehood.
I'm sorry if this is more than your question asked for, but I am not in a position to request that 7 of the current existing countries cease to exist, or for the internationally-agreed-to continental boundaries be moved. Tell the writer of the question to just suck it up and deal with it.