They said that the answer is July 16 but my answer is August 17. Both have a convincing explanation but in order to prove that my answer is correct, i have to disprove the July 16 deduction.
Line #1: Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know too.
Answer says: For Albert to know that Bernard does not know, Albert must therefore have been told July or August, since this rules out Bernard being told 18 or 19.
I say: That's not the only way to conclude that Bernard doesn't know. Without ruling out 18 and 19, Bernard still can't tell the month. The remaining dates, 14, 15, 16, and 17, are all existing in 2 different months. Albert stated line 1 because of that reason. Therefore, ruling out 18 and 19 is unnecessary.
Scenario 1 (july 16): Albert: I got July, so if Bernard gets either 14 or 16, he won't be able to tell Cheryl's exact birthday.
Scenario 2: (august 17) Albert: I got August, so if Bernard gets 14, 15, or 17, he won't be able to tell Cheryl's birthday because they all appear in different months.
Line #2: Bernard: At first I don’t know when Cheryl’s birthday is, but now I know.
Answer says: Bernard has deduced that Albert has either August or July. If he knows the full date, he must have been told 15, 16 or 17, since if he had been told 14 he would be none the wiser about whether the month was August or July. Each of 15, 16 and 17 only refers to one specific month, but 14 could be either month.
I say: Bernard knows? So what's the date Bernard is thinking at this point?
Scenario 1 (july 16): Bernard: I got 16 from Cheryl. So, is it May 16 or July 16? Albert's right. I don't know the answer either. (Bernard will not rule out the months of May and June because he agrees with line 1. For Bernard's point of view, May 16 is still a possible answer. What Albert knows is that it can't be 18 or 19 because he knows the month. But for Bernard, knowing the date can only help him eliminate June and August and still be stuck with 2 possible answers. Line 1 doesn't help him in this scenario.)
Scenario 2 (august 17):
Bernard: I got 17 from Cheryl. That means it's either June 17 or August 17. If it's June, Albert will not say line 1. Instead, he will say that i might know the answer because if i got 18, i will surely know that it's June 18. The fact that he said that I don't know the answer means that it must be in August. Therefore, August 17.
Line #3: Albert: Then I also know when Cheryl’s birthday is.
Answer says: Albert has therefore deduced that the possible dates are July 16, Aug 15 and Aug 17. For him to now know, he must have been told July. Since if he had been told August, he would not know which date for certain is the birthday.
I say: Albert won't be able to think that way because Bernard doesn't know the answer in scenario 1.
ENDING:
Scenario 1 (july 16): Albert: Bernard also thinks he doesn't know. I'm guessing between 2 possible months and he's guessing between 2 possible dates. we both don't know the answer.
Scenario 2 (august 17): Albert: (At this point, i'm guessing whether it's August 14, 15 or 17. How the hell did Bernard find out? I thought there's no way he would be able to find out because it would never be June 18 nor May 19. If he knows the answer, he probably eliminated them as well using his knowledge of the date. He was still confused until i said that he surely doesn't know the answer. Which means he was able to eliminate a potential answer because of my statement. And that's June 17 because even though it was left alone as a possible answer from June, i still said that he won't be able to know the answer. It's true that i'm left with 3 more options but for him, he's left with only 1 answer and that's August 17.) "Then I also know when Cheryl’s birthday is."
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