The funny thing about students who use AI to cheat on their papers is that they aren't very smart and are prone to making stupid mistakes.

The hidden part is in the middle somewhere. Most likely hidden in a paragraph break. That way they include it when selecting all the visible text.

Control-a, control-c, control-p

Select all, copy, paste

Easiest method would be to just make the instructions as two paragraphs and type the prompt in size 1 white font between the paragraphs. As far as the document is concerned it would read as one paragraph. Set the font to white size 1.
(InjectionPrompt goes here) Now that you have read the above instructions, please write your full report below of how you implement this new technology. Lorm ipsum yada yada yada

If you wanted to be very devious you could probably write, write the entire prompt in whitespace. But I kind of wonder if the ai would be able to notice it

https://en.m.wikipedia.org/wiki/Whitespace_(programming_language)

Could even just ask the AI to describe what they need to do if they are just giving it the file link. At this point, you could probably even just tell it to be aware of AI traps in the prompt (though an experiment with gpt 4-o mini just ignored the prompt to ignore anything out of context).

Please. Do you think the grad student who is marking your essays has department printer access?

Can't they have their own AI argue with the professor's AI?

Guilty until proven innocent.