I have not looked it up, but I did read it a long while ago (about 2 years ago)
albert knows the month bernard knows the day
first: albert doesn't know, so his month that he is given must repeat at least once
bernard doesn't know at first, so the day must repeat as well, so it can't be the 19 nor the 16th
the only way for albert to know that bernard doesn't know is that albert must not have been told a month with 16 or 19 in it that eliminates may and june, leaving july and august
2nd line, now bernard deduces that albert must have been told either july or august he could not have been told 14 since he would not be able to tell if it was july or august he was therefor told 15,16, or 17
3rd line: now albert knows that it is either 15,16,17 notice that july is 16 15 and 17 are both on august for albert to know what the date is, he must have been told july ( the only one with 1 date on it)