I noticed that one student is performing exceptionally well and beyond his level during an online class. I was wondering if there are particular chess positions that I can use during class to find out about such cheating. I would like to know of some positions that are easy and logical for humans but would make engines go crazy.
One way to fool some computers is to give them a fortress and then offer material to trick them into opening the portcullis. For example:
[Title "White to draw"] [FEN "8/8/pr1k4/Pp2rp1p/1Pp1pPpP/2PpP1P1/3P4/3K4 w - - 0 0"] 1. fxe5+?? (1. Ke1) (1. Kc1) 1... Kxe5 2. axb6 Kd6 0-1
Many computers won't resist the temptation to win RR for PP, but the resulting pawn ending is lost (Black can play Kb6, a5, a4, and then break through with f4). Instead White can just play random King moves, ignoring any Rook captures, and wait for 50 moves and there's nothing Black can do about it.
It's not exactly your question but could do the trick for your case. Set up mate in one problem involving en passant. Setting up a position with an en passant square is not completely trivial, so your allegedly cheating student could miss one of this type. Here is an example.
[FEN "4rk2/3prp1Q/1p4P1/3Pb2P/2P1pPq1/8/7K/5R1R b - - 0 1"]