A much better example, in my mind, is binary addition. Conceptually, binary addition is very easy to explain (there are two sequences of bits, we want to combin

A much better example, in my mind, is binary addition. Conceptually, binary addition is very easy to explain (there are two sequences of bits, we want to combine them pair wise, etc.), yet it’s trivially easy to double the problem space by adding a single bit. o1 can add up to 10 bits, which would be trivially easy to memoize in its billions of parameters. It really makes you realize that, while LLMs appear smart, they fundamentally lack the ability to handle more than a few independent pieces of information despite their massive size.