Math Puzzle
- Thread starter What Would Jesus Do?
- Start date
This is the answer posted on line. But it's wrong. There's a flaw in their step-by-step analysis. Trust me. I will give the correct answer later on to give everyone a chance.
Or maybe I'm wrong. In which case those who figure it out can have some fun at my expense. I'll just use my usual excuse: not enough coffee.
I am assuming they both have the list of 10 possibilities. So if she tells one of them the month, he still isn't sure what day. If she tells the other one the day, and it is either the 18th or 19th then that guy doesn't need to know anything more.
It's July 16 and Cheryl is a cock-tease.
Albert's first statement means he knows it's a month in which every possible date is a possibility in another month. That rules out all the May and June dates.
Bernards statement means that of the remaining options, he knows it is a date that is only possible in one month. That eliminates July 14 and August 14 and leaves July 16, August 15, and August 17 as the possible answers for Albert to deduce. He knows that it is July so it must be July 16. If it was either of the August dates then he would not know which one it was.
Posted from Rivals Mobile
Albert's first statement means he knows it's a month in which every possible date is a possibility in another month. That rules out all the May and June dates.
Bernards statement means that of the remaining options, he knows it is a date that is only possible in one month. That eliminates July 14 and August 14 and leaves July 16, August 15, and August 17 as the possible answers for Albert to deduce. He knows that it is July so it must be July 16. If it was either of the August dates then he would not know which one it was.
Posted from Rivals Mobile
Let's sort of re-do the dialogue here to make this easier to understand.Originally posted by What Would Jesus Do?:
Took me a while to figure this one out. Have fun.
Albert knows which month. Bernard knows which day.
Albert's statement only tells us that it isn't the 18th or 19th. Correct?
June 17
Alberts statment rules out the 18th and 19th as days because if Bernard knew that the day was either the 18th or 19th he would know the month as well since those days are unique.
Since Bernard Knows the date after the statement by Albert means it now has to be a date that is unique to one month. The only date that fits that is the 17th of June.
Alberts statment rules out the 18th and 19th as days because if Bernard knew that the day was either the 18th or 19th he would know the month as well since those days are unique.
Since Bernard Knows the date after the statement by Albert means it now has to be a date that is unique to one month. The only date that fits that is the 17th of June.
Quoting myself here, but if ALBERT knows that Bernard cannot possibly know the birthday, that means ALBERT was not told May or June. He would know for sure there is no chance Bernard was told the 18th or 19th in that situation.Originally posted by Pepperman:
Let's sort of re-do the dialogue here to make this easier to understand.Originally posted by What Would Jesus Do?:
Took me a while to figure this one out. Have fun.
Albert knows which month. Bernard knows which day.
Albert's statement only tells us that it isn't the 18th or 19th. Correct?
Once Bernard hears this, he knows that the month isn't May or June, meaning it has to be July or August. So at this stage, we have it narrowed down to just 3 possibilities.
Yep.
You have to assume that it's a "fair" puzzle and that the statements made by each person are true. So when the guy who got the date number doesn't instantly know the answer, that rules out the 18th and the 19th.
Let me try to explain it another way.
Albert knows it is in July, so he know it has to be either July 14 or July 16. Albert knows it is the 16th, but doesn't know whether it's May 16 or July 16.
Albert knows that Bernard doesn't know the date because the only two unique dates were the 18th and the 19th and July 18 and July 19 were not options.
Bernard can infer from this that Albert knows it is neither May nor June and must be either July or August. That leaves only July 16 for him, so now he knows for certain it is July 16.
Once Bernard told Albert that he knows correct answer, Albert could deduce that Bernard was able to eliminate July 14 and August 14 and pinpoint it to one of the three remaining unique dates - July 16, August 15, and August 17. So at that point Albert also knew it had to be July 16.
Posted from Rivals Mobile
Albert knows it is in July, so he know it has to be either July 14 or July 16. Albert knows it is the 16th, but doesn't know whether it's May 16 or July 16.
Albert knows that Bernard doesn't know the date because the only two unique dates were the 18th and the 19th and July 18 and July 19 were not options.
Bernard can infer from this that Albert knows it is neither May nor June and must be either July or August. That leaves only July 16 for him, so now he knows for certain it is July 16.
Once Bernard told Albert that he knows correct answer, Albert could deduce that Bernard was able to eliminate July 14 and August 14 and pinpoint it to one of the three remaining unique dates - July 16, August 15, and August 17. So at that point Albert also knew it had to be July 16.
Posted from Rivals Mobile
This is the flaw in the online explanation. This does NOT rule out May.
But it does rule out June. So if Albert had been told that the month was June, he would know the answer. Since he tells us he doesn't know the answer at that point, that means June is not the correct month.
That, as it turns out, is enough info for Bernard to figure out the correct answer. And because he can figure out the correct answer with that fact (not June), we can figure out what number he must have been told.
Both kids have all 10 options before this begins.Originally posted by What Would Jesus Do?:
Took me a while to figure this one out. Have fun.
Albert - who is provided with only the month - initially can't know the birthday because each month has more than 1 date option.
Albert then says he also knows that Bernard also doesn't know.
If Bernard - who is provided with only the date - doesn't know, this must mean he wasn't provided with the unique dates of 18 or 19. So you can eliminate May and June.
Or that's at least what the online answer says. But I disagree with this - you can't eliminate the entire months of May and June, just the unique dates of May 19 and June 18. Unless I am missing something.
I think this is what WWJD is thinking of as the error.
I tend to agree with him, but I must be overlooking something because everyone else says the entire months of May and June can be entirely eliminated by Albert's first statement.
Assuming that the entire months of May and June can be eliminated, the rest falls into place as others have posted in this thread.
Exactly. IF you could rule out May and June, then the arguments made on line and here by others seems right. But here is the actual list of dates after the first round:Originally posted by St. Louis Hawk:
Both kids have all 10 options before this begins.Originally posted by What Would Jesus Do?:
Took me a while to figure this one out. Have fun.
Albert - who is provided with only the month - initially can't know the birthday because each month has more than 1 date option.
Albert then says he also knows that Bernard also doesn't know.
If Bernard - who is provided with only the date - doesn't know, this must mean he wasn't provided with the unique dates of 18 or 19. So you can eliminate May and June.
Or that's at least what the online answer says. But I disagree with this - you can't eliminate the entire months of May and June, just the unique dates of May 19 and June 18. Unless I am missing something.
I think this is what WWJD is thinking of as the error.
I tend to agree with him, but I must be overlooking something because everyone else says the entire months of May and June can be entirely eliminated by Albert's first statement.
Assuming that the entire months of May and June can be eliminated, the rest falls into place as others have posted in this thread.
May 15 May 16 May 19
June 17 June 18
July 14 July 16
August 14 August 15 August 17
All the remaining dates are still viable.
Once Albert realizes that Bernard doesn't know the answer, he knows the 18th and 19th are out. IF he had been told the month was June, THEN he would know the answer. But he says he doesn't know the answer. So that rules out June and the list now looks like this:
May 15 May 16 May 19
June 17 June 18
July 14 July 16
August 14 August 15 August 17
Bernard recognizes that June is out and, based on that, declares he has the answer. The only way he could have the answer at this point is if the number he was given was the only unique number left in the list: 17.
Once Bernard says he knows the answer, Albert follows the logic and also knows the answer.
August 17 is the correct answer.
So Albert knows the month, and by knowing the month, he knows that Bernard cannot know the date. If he was given May or June, he would not know for sure if Bernard knew the date. The statement isn't that Bernard knows the date, the statement is Albert knows he doesn't know the date. Therefore, he must have been given the month of July or August. If it was July or August 14th, Bernard still wouldn't know, but he says he does know. If it was August, he still wouldn't know if it was the 15th or the 17th. Albert knows if Bernard could figure it out, it would have to be July 16th, because he wouldn't have been able to know for sure if it was July 14th.
That's actually an interesting argument that works if you assume that Albert knows Bernard doesn't know (in the first stage) NOT because Bernard didn't already claim to know (which is the way I'm looking at it) but because he was given a month that rules out any possibility of Bernard knowing. A priori vs a posteriori knowledge.
So . . . I now think there are 2 possible correct answers depending on how you interprete the first comment from Albert
August17.
Only July and August have days that are in other months. Thus, only if Albert were told July or August could he be certain Bernard did not know the day. Albert figures it's July or August, but he could only be certain of the month if the day is the 17th otherwise he wouldn't.
This post was edited on 4/15 12:01 PM by pablow
Only July and August have days that are in other months. Thus, only if Albert were told July or August could he be certain Bernard did not know the day. Albert figures it's July or August, but he could only be certain of the month if the day is the 17th otherwise he wouldn't.
This post was edited on 4/15 12:01 PM by pablow
To summarize my new position, I'm now of the opinion that both answers could be correct - depending on whether you interpret Albert's knowledge in the first stage as a priori or a posteriori knowledge.
Does Albert "know" that Bernard doesn't know because Bernard has not
claimed to know the answer (a posteriori knowledge) or because Albert
got a month that rules out Bernard knowing the answer (a priori
knowledge)? The a posteriori knowledge interpretation leads you to
August 17. The a priori knowledge interpretation leads you to July 16.
So . . . better buy Cheryl a present for each of her 2 possible birthdays to be safe.
Does Albert "know" that Bernard doesn't know because Bernard has not
claimed to know the answer (a posteriori knowledge) or because Albert
got a month that rules out Bernard knowing the answer (a priori
knowledge)? The a posteriori knowledge interpretation leads you to
August 17. The a priori knowledge interpretation leads you to July 16.
So . . . better buy Cheryl a present for each of her 2 possible birthdays to be safe.
It's July 16h and that is the only possible answer and I will explain:
After the first statement (Albert says he doesn't know, but does know that Bernard doesn't know either), you can eliminate all of May and all of June.
The only way for Albert to know for sure that Bernard doesn't know the date is for him to be given either July or August.
If Albert was given May, there is a possibility that Bernard would know the date if he was given the 19th. That eliminates all of the May dates since Albert knows for sure that Bernard doesn't know.
If Albert was given June, there is a possibility that Bernard would know the date if he was given the 18th. That eliminates all of the June dates since Albert knows that Bernard doesn't know.
After the second statement, you can eliminate July 14 and August 14.
If Bernard was given the 14th, after Albert's statement, he would still not be able to know if it was July 14 or August 14, so he could not state factually that he knew the date.
For Bernard to know for sure after Albert's statement, it could be July 16 because if he was given the 16th and May 16th was eliminated after the first statement, he would now know. The same logic allows that it could be either August 15 or August 17.
This leaves us with July 16, August 15 and August 17th.
Let's say Bernard was given the 15th or 17th. After Albert's first statement, Bernard would know for sure that the month was August and could say that he knew for sure. However, after Bernard's statement, if Albert was given August, Albert still wouldn't know if it was the 15th or 17th since with either date, Bernard would know for sure. The only way for Albert to know for sure (the third statement) would be for his month to be July.
Done!
This post was edited on 4/15 1:17 PM by at4iowa
This post was edited on 4/16 8:41 AM by at4iowa
After the first statement (Albert says he doesn't know, but does know that Bernard doesn't know either), you can eliminate all of May and all of June.
The only way for Albert to know for sure that Bernard doesn't know the date is for him to be given either July or August.
If Albert was given May, there is a possibility that Bernard would know the date if he was given the 19th. That eliminates all of the May dates since Albert knows for sure that Bernard doesn't know.
If Albert was given June, there is a possibility that Bernard would know the date if he was given the 18th. That eliminates all of the June dates since Albert knows that Bernard doesn't know.
After the second statement, you can eliminate July 14 and August 14.
If Bernard was given the 14th, after Albert's statement, he would still not be able to know if it was July 14 or August 14, so he could not state factually that he knew the date.
For Bernard to know for sure after Albert's statement, it could be July 16 because if he was given the 16th and May 16th was eliminated after the first statement, he would now know. The same logic allows that it could be either August 15 or August 17.
This leaves us with July 16, August 15 and August 17th.
Let's say Bernard was given the 15th or 17th. After Albert's first statement, Bernard would know for sure that the month was August and could say that he knew for sure. However, after Bernard's statement, if Albert was given August, Albert still wouldn't know if it was the 15th or 17th since with either date, Bernard would know for sure. The only way for Albert to know for sure (the third statement) would be for his month to be July.
Done!
This post was edited on 4/15 1:17 PM by at4iowa
This post was edited on 4/16 8:41 AM by at4iowa
I'm not sure why some of you guys are struggling so much with the May issue. If her birthday was any of the May dates then Albert would have known only that it was in May. As far as he knew, Bernard could have been told 15, 16, or 19. He could not know for certain that Albert Bernard did not know the date because if Bernard had been told the 19th then Bernard would have known immediately that it was May 19.
If it had been any of the dates in May then Albert could not have stated with 100% certainty that he knew Bernard didn't know the date.
As soon as Albert made that statement, Bernard knew it had to be either July or August.
Posted from Rivals MobileEdited because I realized I type Albert when I should have type Bernard.
This post was edited on 4/15 3:36 PM by TJ8869
If it had been any of the dates in May then Albert could not have stated with 100% certainty that he knew Bernard didn't know the date.
As soon as Albert made that statement, Bernard knew it had to be either July or August.
Posted from Rivals MobileEdited because I realized I type Albert when I should have type Bernard.
This post was edited on 4/15 3:36 PM by TJ8869
After a little over an hour of reading and re-reading the July 16th crowds logic and starting a couple posts supporting August 17, I am now fully on board the July 16th train. And my head hurts. I need a drink.
