how do you make a java applet?

Whoops ya I didn't really search for applets They seem a lot of work. Are there any other options?
The javascript form looks promising, I'll look a bit into that.

And I don't know php only java

Well javascript is kind of very similar to java syntax-wise... the functions you can use are sort of limited and i dont think you can import libraries, but the main difference is that you code it into the HTML. for example:
<script language="JavaScript" type="text/javascript">
function solve()
{
//get input from the text boxes using getElementById, output it either using alert() or through another text box.
}
</script>
<input type="submit" value="Solve" onclick="solve()">


also @kajiti, i have no idea how the stage works (in fact, i never did a GPQ), but considering the little options you have you can always just brute force it if nothing else succeeds.