From the FAQ:
* Which version of SDK should I use?
Your submission should have something like this:
(...) the submission that you return must have been tested and
shown to work under a production (not development) version of
the Sun Microsystems' Java 2 plataform and that plataform must
not have been superseded by a new production version for more
than 18 months by the time you make your submission.
You may use the link in the next question and do the math. When in doubt, just use the latest version.
Example calc: I want to use 1.4.1, but 1.4.2 (the right next version, although 1.5 is also released) has already been released on June 26, 2003. Adding 18 months to that, around January 26, 2005. So if you upload your assignment before that, you are ok.
* How can I find out when a version of the JDK was released? http://java.sun.com/j2se/codenames.html