This interesting puzzle is something that will appeal to any logical reconstructionist  that comes across it. I swear its interesting to anyone with mathematical and logical upbringing. So when I saw it a day or two ago I wanted to know what the fuss is all about. Luck had it that I could not go to work today for some reason. I got some free time and checked it out. Couple others had sprouted it along on social sites.

So given the little free time — and my ISP came back today after couple weeks, after a patient call to customer service, I wanted to look into the problem. Its in the nature of internet these days anything that creates enough vibe will be on your desk for a while if you are a regular surfer that you know why certain things are viral. One of the things I never laid my attention on was the “gold and white apparel” of recent times, perhaps one of the reasons above was not in my favor: free time or swift painless internet.

Now that I could lean back I guessed the answer for this puzzle after reading it a couple times mindfully. I think the answer is August 17. WHY? I will explain in detail. But first of all the answer I came across here (in NY Times) is obviously misleading and incorrect. They give July 16 as the answer, but their method is wrong because they eliminated both May and June and there isn’t enough information for such a step. What they should do is eliminate May 19 and June 18. Because these two dates (18, 19) are not duplicated in the list of dates. Once they did so it would be clear from the conversation between Albert and Bernard that June 17 could also be eliminated.

Because since Albert knows that June 18 and May 19 are not good candidates for DOB, neither can June 17 be. If June 17 was the date he would not claim “I don’t know the date of birth” because he already knows the month and there is only one date in this month that is June 17. Obviously June 17, 18 and May 19 are to be discarded. In rest of the list only one date; August 17, appears once, all others appear twice. If August 17 were NOT to be correct Bernard can not claim that he knows the date of birth NOW. Hence answer is August 17.

[In short; Only single dates and single month can be eliminated because that would make either A or B know the answer, since they don’t know at first, single dates are June 18 and May 19 and single month is June 17 (after first round of elimination) Hence once these dates are eliminated from birthday-answer, what we have is August 17, a single date, as the answer is now known by B and as a consequence by A.]

———- A little more feeder for the conversation between Albert and Bernard.

Hint 1; Cheryl tells Albert: MONTH and Bernard: DATE.
Obviously this general fact is known by both Albert and Bernard.
So Albert knows “I know the month Bernard knows the date”.
Same goes with Bernard “I know the date and Albert knows the month”.
From that base the conversation is a logical exchange of information although not so obvious. An example of how language can be made to sly with logic.
Hint 2; There is another trick hidden here.
First either Albert lied when he said “I don’t know, neither does Bernard” and Bernard believed him.
Or in retrospection Cheryl told Albert “You know I have told you month and Bernard the date, but rest assured he doesn’t yet know my date of birth”.
Situation 1; So it may be just that Albert lied (or rather tricked Bernard to believe him and conform that indeed June 18 and May 19 are not good dates.)
Situation 2; If he did not lie — as per NY times article, there still is the possibility that Cheryl tells Albert the month and the fact that Bernard although knows the date, knows not the date of birth yet, that will save the grace for all and make it purely logical than one of anthropic misunderstandings.
In any case as per logic then obviously May 19 and June 18 are to be eliminated and not June and May months altogether. That would be a big mistake. Once 19 and 18 are removed in Bernards mind June 17 is not a good date because that’s the only date in month of June and Albert knows the month and he says he knows May 19 and June 18 are not the dates, so he can’t claim “I don’t know”. What remains as a good date is August 17 in order to match with the 3 statements.