My first eye-opener about 1-way functions is this algorithm: Take a word. Remove every second letter. This is a one-way function, because it's basically impos

My first eye-opener about 1-way functions is this algorithm: Take a word. Remove every second letter. This is a one-way function, because it's basically impossible to recover the original, even for two letter words. It's not a very good as a one way hash, because you can trivially construct collisions. It does, however, nicely capture the idea that you are pretty much always going to be discarding information to get a hash (if the hash is shorter than the input), without really resorting to the pigeonhole principle.