There are several websites around the world that provide example problems and many of these also have "on-line judges" to which you can submit your trial solutions. Your submissions are marked automatically and you can resubmit until your program is working. If you can't get your program working, or can't even figure out how to begin, you might have to read some books on algorithms.

Some websites you might want to check out are:

• Sphere online judge (SPOJ) is a Polish website with a respository of nearly 2000 problems covering a wide range of difficulties and algorith types. Registration is free and you can submit programs in a wide range of languages. The SPOJ system has been around since 2004, with over 30000 registered users and 1.7 million submissions to date.
• The High School Programming League is a programming contest run by the SPOJ staff (see the previous item). The contest consists of seven problem sets, each lasting about 5 weeks. The first problem set opened on September 20 and will last till October 25. More than 500 participants have already started solving problems, but it is still possible to join the contest.
• The Competitive Learning Institute's ACM-ICPC Live Archive is a collection of actual programming contest problem sets. Although the sets relate to the ACM international computer programming contest, in which problem sets are solved by teams of three rather than by individuals as with the IOI, the problems still provide excellent practice. Select the Oceania region if you want to feel at home! You can submit solutions in C, C++, Pascal and Java.
• The Universidad de Valladolid's UVa Online Judge site is an excellent training repository of over 2000 problems, with over 6 million submissions to date. Each problem has statistics on the number of submissions and their success rates, allowing you to select easier or harder problems according to your needs.