It would not work for arbitrary inputs. See the pigeonhole principal: you can’t represent all possible n-bit values with fewer than n bits, because otherwise yo

It would not work for arbitrary inputs. See the pigeonhole principal: you can’t represent all possible n-bit values with fewer than n bits, because otherwise you’d have at least one case where multiple input values map to the same output value. On decompression, which one do you go with? And if that’s not convincing, then consider that any perfect compression scheme would be able to compress its own output even smaller, until you end up with a single bit output for any possible input. So no, that wouldn’t work in general. Some specific values may compress well, but most others can’t. It’s not a matter of difficulty of finding the right answers, as much as you probably can’t do it.