If you know someone else doesn't know, that just gives you more knowledge you yourself can use.

For the "hardest puzzle", on each day everyone learns that no one was able to figure out the solution the day before. Because of this, a person knows that for a possible number of blue-eyed people to be valid, a person who sees one less blue eyed person than that, must have been unable to figure it out on the previous day.

An Arc/Common Lisp solution I just wrote up: https://gist.github.com/malisper/80625bcda75c66780f81