Logic question on finding age of someone

[chwala]

Homework Statement

Homework Equations

The Attempt at a Solution

the solution according to blog is

Neither May nor June is possible because they have unique dates - that means Albert couldn't know for sure that Bernard doesn't know. If Albert had May for example, Bernard might have the number 19 and Bernard would know the date. But Albert knows for sure that Bernard doesn't know.

Bernard understood that ^ and said he now knows the answer. Threfore, his day must be among those that occurred in May or June as well. Hence, it can be neither July 14th nor August 14th.

Albert now understood the consequences of the upper statement and realized he knows the date: hence, it must be July 16th. If his month was August, he couldn't have said for sure.

i don't understand kindly assist me on this

 

[Orodruin]

What part of the argument do you not understand?

 

[chwala]

how did he arrive at the date being july 16th...lol am dumb on this. What does unique dates mean in the context of may and june? i think am now getting it, does it borrow from conditional probability, analysis from the first months to the last?if not 1 then 2, ...if not 2 then look at the possibilities of 3?

 

[Orodruin]

There is no probability involved here, just logic. You already have the answer so unless you dpecify exactly which part of the argument you are having trouble with it is going to be impossible to assist you.

 

[haruspex]

Let's take the first step.
Albert says he knows that Bernard does not know the exact date, even though he knows that Bernard does know the day of the month. Could the month be May? If Albert knows the month is May, then as far as he knows it could be May 19. But if it is May 19 then Bernard would know the month too, because no other possible date is a 19th. Yet Albert is confident that Bernard does not know, so Albert must know it is not May.

 

[chwala]

Albert says he knows that Bernard does not know the exact date, even though he knows that Bernard does know the day of the month. i don't understand this statement clarify and as far as he knows why not may 15th?
explain this in a way i can understand, i have stated that on this logic am seeing stars...

 

[haruspex]

Albert says he knows that Bernard does not know the exact date, even though he knows that Bernard does know the day of the month. i don't understand this statement clarify exact date or exact month and as far as he knows why not may 15th?

Yes, it could be May 15th, but what matters is that could be May 19th.
Suppose Bernard had been told 19th. Bernard would then immediately know it was May 19th. Albert understands this. So how can Albert be sure that Bernard is unable to determine the month? For Albert to be able to deduce that, he must be able to rule out May 19th. But all Albert knows is the month. If that allows him to rule out May 19th then the month cannot be May.

 

[chwala]

Yes, it could be May 15th, but what matters is that could be May 19th.
Suppose Bernard had been told 19th. Bernard would then immediately know it was May 19th.....this is clear...kindly go on with the explanation arriving at july 16th, i am not strong on logic

 

[haruspex]

Yes, it could be May 15th, but what matters is that could be May 19th.
Suppose Bernard had been told 19th. Bernard would then immediately know it was May 19th.....this is clear...kindly go on with the explanation arriving at july 16th, i am not strong on logic

In exactly the same way we can rule out June because it is the only month with an 18th.
Bernard heard Albert's statement and can follow the same logic that we have, ruling out May and June. So abernard can now focus on the five dates in those two months.
Bernard knows the day of the month, and we now know it must be 14th, 15th, 16th or 17th. Suppose it is 14th. Does Bernard now have enough information to determine the month?

 

[chwala]

Thanks Haruspex, the logic is to rule out any hints that may enable Bernard get the date, hence the month...now clear, it can't be 14th because there is more than one possibility and neither 15th nor 17th, hence the only possible date and month is 16th July. greetings from AFRICA

 

[haruspex]

neither 15th nor 17th

You are right, but how did you deduce that?

 

[chwala]

Two months are having dates 15th and 17th respectively which implies that Bernard won't know with certainity which month it is.
by logic.

 

[haruspex]

Two months are having dates 15th and 17th respectively which implies that Bernard won't know with certainity which month it is.
by logic.

No, you are forgetting that Bernard has already ruled out May and June by this point. If it were 15th, Bernard would now know it was August 15th. You need to use the final piece of information.

 

[chwala]

Ok, going with that reasoning we will rule out August because of the same reason why we ruled out May, right? If the date was 17th or 15th then Bernard would know the month, hence the reason of ruling out August and on considering the 14th date, Bernard will not know for sure which month it is, leaving us with the only possibility of July 16th, right?

 

[haruspex]

Ok, going with that reasoning we will rule out August because of the same reason why we ruled out May, right? If the date was 17th or 15th then Bernard would know the month, hence the reason of ruling out August and on considering the 14th date, Bernard will not know for sure which month it is, leaving us with the only possibility of July 16th, right?

I didn't follow that at all, but I'm pretty certain it's wrong because you did not mention the piece of information you need to use.

 

[chwala]

what do you mean?
I am aware that Albert is certain on the month and Bernard is certain on the date, as you said for Albert to be sure that Bernard does not know that its May with the reason
If Albert knows the month is May, then as far as he knows it could be May 19. But if it is May 19 then Bernard would know the month too, because no other possible date is a 19th.
Suppose Bernard had been told 19th. Bernard would then immediately know it was May 19th. Albert understands this. So how can Albert be sure that Bernard is unable to determine the month? For Albert to be able to deduce that, he must be able to rule out May 19th. But all Albert knows is the month. If that allows him to rule out May 19th then the month cannot be May.

it is with this same reasoning that i concluded

If the date was 17th or 15th then Bernard would know the date and consequently the month, hence the reason of ruling out August, is this statement correct?

 

[haruspex]

If the date was 17th or 15th then Bernard would know the date and consequently the month, hence the reason of ruling out August,

No, you need to be careful about who knew what when.
At the start, before Albert's first statement, if it was 17th or 15th, Bernard would not know the month. At that stage, he cannot rule out May or June.
Bernard was only able to rule out May and June when he heard Albert's first statement, and he could do that whether it was July 16, Aug 15 or Aug 17.
To work out which of those, you need to use the final piece of information:

Albert: Then I also know when Cheryl's birthday is.​

 

[chwala]

Ok lol, logic has always been a pain to me...thanks..