Yeah, that was my first solution. When I mentioned this to a colleague of mine, they suggested an optimisation where you flip the card white, not only on your day but, on the days of the kids you
already know have gone through. This will propogate the information faster...
For all of you who are looking for a more in-depth treatise of this problem, check out this PDF file of
a problem with a hundred prisoners...
EDIT: Damnit, I forgot to double-check my link. It's been corrected now...