Okay, I'll attempt to clear up the confusion between two different events. I'm paraphrasing, so I might have the order a bit messed up, but basically, the fish/dance incident was the 10th exam, the handprint/salute was the 11th. It happened something like this:

Rimmer and Lister are in their room, Rimmer has written all over his arms and legs with ink and is quizzing himself outloud and comparing his answers to those on his body. He then works out the percentage of the exam each section of his body is worth. Lister walks in and they discuss the 10th time Rimmer flunked his engineering exam, about which bus ridin' fool explains nicely.

Lister: Whatch'ya doin'?
Rimmer: I'm studying for my engineering exam.
Lister: By writing on your body? Wouldn't that be cheating?
Rimmer: It's not cheating, it's simply an aid to memory.
Lister: I know! Why don't you hand your body in and let them mark that?
Rimmer: You wouldn't understand, Lister, what it's like... (insert Rimmer-rant here, where he complains about how nothing's fair)
Lister: What's the point, though? You're just gonna go in there and flunk again.
Rimmer: For your information Lister, I only failed last time by the narrowest of narrow margins.
Lister: Narrowest of narrow margins?! You walked in, wrote "I am a fish" 400 times, did a funny little dance and fainted!
Rimmer: I did not.
Lister: Yes you did. Petersen told me.
Rimmer: (mimics Lister) Petersen told me. (normally) If you must know, I wrote a discourse on porous circuits that was simlpy too radical, too unconventional, too mold-breaking for the examiners to accept.
Lister: Yeah, you said you were a fish.

Eventually, it is time for Rimmer to leave to takes his exam for the 11th time. He is convinced he is prepared, until he gets the exam. To his terror, the exam looks to be only a single question. He flips the page over. It's blank. He trys to peel it apart in case there are two pages stuck together. Just one page, one question. He starts to panic, and in panicking, starts to sweat. This dissolves the ink. When he rolls up his sleeve to look at the answers on his arm, he finds the ink has smeared all oover his palm. He makes a face that must be seen to be believed, and looks back down at his exam.

So we get to Tosta Dojen's w.u. Rimmer realizes he's screwed, so hoping that maybe, just maybe, the bit on his hand is the answer to the question, and that it remains in a legible form, he slaps his hand down on the paper leaving a single black handpint, stands up, does his salute, and passes out. And he flunks for the 11th time.