So far I've only seen examples based on tokenization ("what's the third letter in word?"), and the fact that answers are generated sequentially ("write a sentence that mentions its own word count"). But those feel unsatisfactory, like asking a human to decode ASCII.
I've personally seen some impressive feats from simple LLMs, like writing sensible code in a new language based only on a few surrounding lines. That shows a level of expertise beyond the common line "it's just mixing sentences from the training data".