I don't see how pigeonhole principle applies to that situation. It could well be that "zero" hashes to 1, "one" hashes to 2... and "f" hashes to 0, extended out

I don't see how pigeonhole principle applies to that situation. It could well be that "zero" hashes to 1, "one" hashes to 2... and "f" hashes to 0, extended out to the hash's length.