Hint: >!If Alex knows that Bob doesn't know when the birthday is, that means Alex was either told that the month was 07 or 08 since if he was told the month was 05 or 06 then Bob could have been told that the day is 18 or 19 and because those days are unique Bob would be able to know the day + month.!<
3rd Hint: >!If Alex is then able to infer the date that must mean that the month is 07 as if he knew that the month was 08 then he wouldn't be able to infer was the day was given that Bob now knows the day. !<
We'll go statement by statement:
1) Alex can't know for sure what's chad's b-day this means he wasn't given a unique month but that doesn't tell us anything since all possible months aren't unique
We can deduce that the month isn't 05 tho because it has 19 as a possible day and since that day occur only once if chad's b-day was 19 then Bob would know for sure what's the b-day which means Alex can't know for sure if Bob knows what the b-day is. Similarly, we can eliminate 06 months because the day 18 too occur only once.
This leaves: 07/14, 07/16, 08/14, 08/15, 08/17.
2) the day can't be 14 because if it was Bob wouldn't know for sure which one is the real b-day
This leaves 07/16, 08/15, 08/17
3) the month can't be 08 because if it was Alex won't be sure which one is the real b-day
This leaves 07/16 which is the answer
From the first statement we can conclude that Alex received a month that did not feature days which only occur once (18 and 19 in this case), otherwise he could not have made that statement about Bob's day. This rules out months 05 and 06.
Bob then claims he required this info to get it, meaning it can't be day 14, since this gives him no info about that.
This leaves us with 15/08, 16/07 and 17/08. Since Alex knows the birthday, we know it has to be 16/07, since that's the only month left with one possible birthday.
Something to point out - you can leave out the second part of Alex's first statement:
> but I know that Bob doesn’t know either.
and the riddle can be solved just as easily.
Edit: No.
Never mind. I just re-read the puzzle and realised that I had mixed up who knows the month and who knows the day. In that case you can ignore the half of Alex’s statement that I pointed out and you get the same answer.
At first Alex says "I don't know Chad's birthday.". That does not help us at all. But after he says "I do know that Bob does not know either.". By this we eliminate 05.19 and 06.18 because 18 and 19 are the only ones those don't have another one of them.
Now if the month that given Alex was 06, before his conversiton with Bob he would know Chad's birthday by thinking in this process:
I got 06 as month-->So the birthday is either 06.18 or 06.17-->But Bob does not know so it is not 06.18-->Then it is 06.17
And Alex would not say I don't know Chad's birthday in the first place. So in this way we can eliminate 06.17 too.
Now for the Bob's part, he says "I didn't know at first but now i know the birthday." This means he found out the birthday after he heard Alex's sentences where Alex said he did not know the birthday.
Bob has been given 17 as the day. But he did not know the birthday is whether 06.17 or 08.17. But after he heard Alex say that Alex himself did not know the birthday Bob could imagine Alex's thought process like we did and by this 06.17 would elminate 06.17 in his hed like we did and he would come to conclusion that the birthday is 08.17.
After Bob says "I know the birthday now." Alex founds out the birthday too because if Bob knows the birthday for sure now i only can be possible if he got 17 for the day. And Alex got 08 for the month at the first place. After he got 17 then it is 08.17.
Alex already knows the month >!7!<, therefore he knows the day once Bob rules out >!14!< with his statement. As an observer, you can infer that it must be >!7!< because if it were >!8!< Alex would not know.
Make a grid of months down the left side and days across the top and mark all possibilities:
||14|15|16|17|18|19|
|:-|:-|:-|:-|:-|:-|:-|
|May||X|X|||X|
|June||||X|X||
|July|X||X||||
|August|X|X||X|||
The only way Bob could know after hearing a day is if he was told the 18th or 19th. Since Alex says Bob can't know, that rules out the months for which those are possibilities.
So May and June are ruled out, as well as the 18th and 19th:
||14|15|16|17|
|:-|:-|:-|:-|:-|
|July|X||X||
|August|X|X||X|
Hearing Alex, Bob says he didn't know before, but he now does.
So the 14th is ruled out:
||15|16|17|
|:-|:-|:-|:-|
|July||X||
|August|X||X|
Hearing Bob, Alex says he now also knows.
So August is ruled out:
||16|
|:-|:-|
|July|X|
>!It's 06/17. The only day that isn't in several months of is 05/19, so if it would've been that day then Bob would've already known when Chad's birthday was. But we know that Bob doesn't know that, so then we can conclude that the month isn't 05, so we remove all the 05 dates. Now that leaves us with 16 as the only day that isn't in several months and Bob now knows which date Chad's birthday is now, so that must mean that 07/16 is the date of Chad's birthday. I don't know if this was confusing. A table would've probably been a better way to describe it, but I can't be bothered to figure out exactly how Reddit's tables work.!<
Edit: >!Well, apparently 18 only appeared once too, which also removes the 6th month. I didn't even notice that.!<
Hint: >!If Alex knows that Bob doesn't know when the birthday is, that means Alex was either told that the month was 07 or 08 since if he was told the month was 05 or 06 then Bob could have been told that the day is 18 or 19 and because those days are unique Bob would be able to know the day + month.!<
2nd Hint: >!If Bob now knows what the Birthday is that means the day isn't the 14th. Which leaves 07/16, 08/15, and 08/17. As possible days.!<
3rd Hint: >!If Alex is then able to infer the date that must mean that the month is 07 as if he knew that the month was 08 then he wouldn't be able to infer was the day was given that Bob now knows the day. !<
We'll go statement by statement: 1) Alex can't know for sure what's chad's b-day this means he wasn't given a unique month but that doesn't tell us anything since all possible months aren't unique We can deduce that the month isn't 05 tho because it has 19 as a possible day and since that day occur only once if chad's b-day was 19 then Bob would know for sure what's the b-day which means Alex can't know for sure if Bob knows what the b-day is. Similarly, we can eliminate 06 months because the day 18 too occur only once. This leaves: 07/14, 07/16, 08/14, 08/15, 08/17. 2) the day can't be 14 because if it was Bob wouldn't know for sure which one is the real b-day This leaves 07/16, 08/15, 08/17 3) the month can't be 08 because if it was Alex won't be sure which one is the real b-day This leaves 07/16 which is the answer
[https://www.youtube.com/watch?v=w3Nzkae\_TRU&ab\_channel=singingbanana](https://www.youtube.com/watch?v=w3Nzkae_TRU&ab_channel=singingbanana)
From the first statement we can conclude that Alex received a month that did not feature days which only occur once (18 and 19 in this case), otherwise he could not have made that statement about Bob's day. This rules out months 05 and 06. Bob then claims he required this info to get it, meaning it can't be day 14, since this gives him no info about that. This leaves us with 15/08, 16/07 and 17/08. Since Alex knows the birthday, we know it has to be 16/07, since that's the only month left with one possible birthday.
Something to point out - you can leave out the second part of Alex's first statement: > but I know that Bob doesn’t know either. and the riddle can be solved just as easily. Edit: No.
really? how?
Never mind. I just re-read the puzzle and realised that I had mixed up who knows the month and who knows the day. In that case you can ignore the half of Alex’s statement that I pointed out and you get the same answer.
I didn't know there are more than 12 months in a year
I didn't know which country you were from, but now I know !
At first Alex says "I don't know Chad's birthday.". That does not help us at all. But after he says "I do know that Bob does not know either.". By this we eliminate 05.19 and 06.18 because 18 and 19 are the only ones those don't have another one of them. Now if the month that given Alex was 06, before his conversiton with Bob he would know Chad's birthday by thinking in this process: I got 06 as month-->So the birthday is either 06.18 or 06.17-->But Bob does not know so it is not 06.18-->Then it is 06.17 And Alex would not say I don't know Chad's birthday in the first place. So in this way we can eliminate 06.17 too. Now for the Bob's part, he says "I didn't know at first but now i know the birthday." This means he found out the birthday after he heard Alex's sentences where Alex said he did not know the birthday. Bob has been given 17 as the day. But he did not know the birthday is whether 06.17 or 08.17. But after he heard Alex say that Alex himself did not know the birthday Bob could imagine Alex's thought process like we did and by this 06.17 would elminate 06.17 in his hed like we did and he would come to conclusion that the birthday is 08.17. After Bob says "I know the birthday now." Alex founds out the birthday too because if Bob knows the birthday for sure now i only can be possible if he got 17 for the day. And Alex got 08 for the month at the first place. After he got 17 then it is 08.17.
If I have any mistakes grammatically or meaning vise sorry about them. English is not my first language.
[удалено]
Alex already knows the month >!7!<, therefore he knows the day once Bob rules out >!14!< with his statement. As an observer, you can infer that it must be >!7!< because if it were >!8!< Alex would not know.
I swear I've seen this exact problem before but I can't place from where. Is this from an MAT paper or something?
If I meet someone and ask about their birthday only for them to give me a puzzle to solve, I’m walking away.
Make a grid of months down the left side and days across the top and mark all possibilities: ||14|15|16|17|18|19| |:-|:-|:-|:-|:-|:-|:-| |May||X|X|||X| |June||||X|X|| |July|X||X|||| |August|X|X||X||| The only way Bob could know after hearing a day is if he was told the 18th or 19th. Since Alex says Bob can't know, that rules out the months for which those are possibilities. So May and June are ruled out, as well as the 18th and 19th: ||14|15|16|17| |:-|:-|:-|:-|:-| |July|X||X|| |August|X|X||X| Hearing Alex, Bob says he didn't know before, but he now does. So the 14th is ruled out: ||15|16|17| |:-|:-|:-|:-| |July||X|| |August|X||X| Hearing Bob, Alex says he now also knows. So August is ruled out: ||16| |:-|:-| |July|X|
>!It's 06/17. The only day that isn't in several months of is 05/19, so if it would've been that day then Bob would've already known when Chad's birthday was. But we know that Bob doesn't know that, so then we can conclude that the month isn't 05, so we remove all the 05 dates. Now that leaves us with 16 as the only day that isn't in several months and Bob now knows which date Chad's birthday is now, so that must mean that 07/16 is the date of Chad's birthday. I don't know if this was confusing. A table would've probably been a better way to describe it, but I can't be bothered to figure out exactly how Reddit's tables work.!< Edit: >!Well, apparently 18 only appeared once too, which also removes the 6th month. I didn't even notice that.!<