My favorite test is to just ask it to add two very large numbers or do other math of that sort. (this is also part of my favorite answer to the chinese room).

You'd be surprised how few digits you need to make a problem that is presumably unique in earth history. For a typical sum, the number of pre-existing answers would need to scale with 10^n lines of text where n is the number of digits. This expands out of control REALLY quickly. A quick guesstimate has you somehow reading out of a literal black hole at n=21 digits if your LUT is on paper, or n=26 digits if you're using modern HDD technology. O:-)