Albert knows the month, Bernard knows the date. If Bernard had 18 or 19, he would know the birthday. For no one to reveal at first, means May 19 and June 18 are eliminated. For Albert to say what he says, he knows it has to be a unique month but duplicate date ie June, but Bernard would not tell if its 17th June or Aug, until Albert said that first statement. I think its June 17th.

I started, like you, with B. If he had been given either 18th or 19th as C’s birthday he would have worked it out. Since the 18th and 19th feature only in May and June, A must have been given either July or August otherwise he couldn’t deduce that B doesn’t know. Do you agree?

As soon as A makes that deduction, it leaves just five dates with 14th featuring twice. If C had told B it was the 14th Bernard wouldn’t know which month it was so he couldn’t have been told that. Likewise if A had been told August then he wouldn’t know either because there are two possible dates in that month.

By my reckoning therefore C was born on 16th July but, as I said, I could be wrong!

If B doesn’t have 18 or 19, it doesn’t rule out May or June as he could have had 15,16 or 17.
That’s where I have a problem with the mathematicians and your solution.
My head hurts!!

May and June are ruled out because A says he ‘knows’ B doesn’t have the answer. If C had told A it was May or June he would have to admit that B ‘may’ know the answer as May and June both have exclusive dates (ie 18th and 19th). QED I think!

Joining this particular headache late in the day, but how is this:-
For A to say he knows B does not know means that it cannot be a unique date, so not 18th or 19th.
If 18th is ruled out, then that leaves only 17th June in June, so June 17th must be ruled out or A would know, and he says he doesn’t.
If 17th June is ruled out then 17th August must also be ruled out as that becomes a “unique” date as the other 17th has gone.
That leaves 6 possible dates – 15/16 May, 14/16 July and 14/15 August.
Then B, who knows the date, says he did not know “at first” that must mean before all the “logic” we have just done above. In other words, eliminating one of dates in one of the months with 3 dates in it would not have helped him “at first” because there would have been 2 dates in those months left and he would not have known which one it was.
Therefore, we have to discount May and August.
This leaves July 14/16.
Let us go back a stage and reinstate as an “imaginary” month August, but discount May (although we really know it is July). The reason we reinstate August not May is because with May we know “at the outset” (or very close to it) that it cannot be 19th as that is a unique date, meaning that if we could discount the other date in May we would have the answer. There is no “unique” date in August, so knowing that it is not one date in August at the outset does not help us.
So we have July and the “imaginary” August, but of those knowing it is 14th does not help, because it could be either month, so it cannot be 14th.
Therefore it must be 16th.
Using the previous workings, we know it has to be July, so applying the lot, it has to be July 16th.
Flip! I need a beer!
Cheers,
Philip

Albert knows the month, Bernard knows the date. If Bernard had 18 or 19, he would know the birthday. For no one to reveal at first, means May 19 and June 18 are eliminated. For Albert to say what he says, he knows it has to be a unique month but duplicate date ie June, but Bernard would not tell if its 17th June or Aug, until Albert said that first statement. I think its June 17th.

I make it July 16th Jonathan but I could be wrong! I’ll post my logic later when I have the time. I’m off for an early morning run now.

I started, like you, with B. If he had been given either 18th or 19th as C’s birthday he would have worked it out. Since the 18th and 19th feature only in May and June, A must have been given either July or August otherwise he couldn’t deduce that B doesn’t know. Do you agree?

As soon as A makes that deduction, it leaves just five dates with 14th featuring twice. If C had told B it was the 14th Bernard wouldn’t know which month it was so he couldn’t have been told that. Likewise if A had been told August then he wouldn’t know either because there are two possible dates in that month.

By my reckoning therefore C was born on 16th July but, as I said, I could be wrong!

If B doesn’t have 18 or 19, it doesn’t rule out May or June as he could have had 15,16 or 17.

That’s where I have a problem with the mathematicians and your solution.

My head hurts!!

May and June are ruled out because A says he ‘knows’ B doesn’t have the answer. If C had told A it was May or June he would have to admit that B ‘may’ know the answer as May and June both have exclusive dates (ie 18th and 19th). QED I think!

But B will only know the answer if it was 18 or 19. Therefore it could still be 15,16 or 17. So strictly the logic still isn’t correct.

If B has 2, 3 or 4 possibles, you could say that he “may” know the answer.

Joining this particular headache late in the day, but how is this:-

For A to say he knows B does not know means that it cannot be a unique date, so not 18th or 19th.

If 18th is ruled out, then that leaves only 17th June in June, so June 17th must be ruled out or A would know, and he says he doesn’t.

If 17th June is ruled out then 17th August must also be ruled out as that becomes a “unique” date as the other 17th has gone.

That leaves 6 possible dates – 15/16 May, 14/16 July and 14/15 August.

Then B, who knows the date, says he did not know “at first” that must mean before all the “logic” we have just done above. In other words, eliminating one of dates in one of the months with 3 dates in it would not have helped him “at first” because there would have been 2 dates in those months left and he would not have known which one it was.

Therefore, we have to discount May and August.

This leaves July 14/16.

Let us go back a stage and reinstate as an “imaginary” month August, but discount May (although we really know it is July). The reason we reinstate August not May is because with May we know “at the outset” (or very close to it) that it cannot be 19th as that is a unique date, meaning that if we could discount the other date in May we would have the answer. There is no “unique” date in August, so knowing that it is not one date in August at the outset does not help us.

So we have July and the “imaginary” August, but of those knowing it is 14th does not help, because it could be either month, so it cannot be 14th.

Therefore it must be 16th.

Using the previous workings, we know it has to be July, so applying the lot, it has to be July 16th.

Flip! I need a beer!

Cheers,

Philip