Logic riddle gone viral (math-ish)

[Blzer]

Let me begin by saying this problem is probably everywhere online, so be the honest person and don't think that just because you can figure out the answer that you're automatically into "cool" status on here. Better yet, please don't spoil it for the rest of us. I e-mailed this to my math staff, and a teacher blurted out an answer in response without any valid reasoning. Even if she is right, I don't know how she stumbled on it. Please leave any answers or work for it in spoiler tags.

A student presented me with this problem today. He did not say whether he figured out the answer to this himself, but he said he knew the answer to it. I only spent five minutes with it before I had to stop, and even though I made progress with it I still hit a roadblock.

Here it is! It's not a trick question and supposedly there is only one real answer.

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Albert and Bernard just become friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.

May 15, May 16, May 19
June 17, June 18
July 14, July 16
August 14, August 15, August 17

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Albert: "I don't know when Cheryl's birthday is, but I know that Bernard does not know too."
Bernard: "At first I don't know when Cheryl's birthday is, but I know now."
Albert: "Then I also know when Cheryl's birthday is."

So when is Cheryl's birthday?

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Good luck!

[Antec]

Re: Logic riddle gone viral (math-ish)

Neat Riddle. Not easy but at the same time very solvable.

[Blzer]

Re: Logic riddle gone viral (math-ish)

I'm certain it is. Still haven't looked at it yet, but here are the dates I have it down to so far (this was from earlier today):

Spoiler

May 15, May 16
July 14, July 16
August 14, August 15

• Albert knows it’s not June 18th or May 19th, because then Bernard would know what the date is.
  
• Bernard knows that Albert knows it’s not June 18th or May 19th, so Bernard knows that it can’t be in June because then Albert would know when it is, which means it’s not June 17th.
  
• Albert knows that Bernard knows it’s not June 17th, and the only other month with the 17th is August 17th. Albert knows that Bernard doesn’t know when it is, so Albert knows it can’t be August 17th either.

This is, of course, where it gets difficult to figure out exactly where to go from here.

[LowerWolf]

Re: Logic riddle gone viral (math-ish)

I googled and read the official answer, but it doesn't make sense to me.

I'm putting the answer and my thoughts in the spoiler, so don't read if you don't want to know yet:

Spoiler

July 16th is given as the official answer, but ...

Albert knows the month. Bernard knows the date. Albert says he doesn't know but he knows Bernard doesn't know. So, you can rule out May 19th and June 18th. Those are unique days, so Bernard would know if it was one of those.

Next, you can rule out June 17th. Albert knows its not the 18th, so he would know if it was June 17th.

That leaves: May 15/16, July 14/16 and August 14/15/17.

Bernard says he now knows the answer. Since August 17th is the only unique date left, that has to be it, right?

[kehlis]

Re: Logic riddle gone viral (math-ish)

I googled and read the official answer, but it doesn't make sense to me.

I'm putting the answer and my thoughts in the spoiler, so don't read if you don't want to know yet:

Spoiler

July 16th is given as the official answer, but ...

Albert knows the month. Bernard knows the date. Albert says he doesn't know but he knows Bernard doesn't know. So, you can rule out May 19th and June 18th. Those are unique days, so Bernard would know if it was one of those.

Next, you can rule out June 17th. Albert knows its not the 18th, so he would know if it was June 17th.

That leaves: May 15/16, July 14/16 and August 14/15/17.

Bernard says he now knows the answer. Since August 17th is the only unique date left, that has to be it, right?

I spent far too much time on this than I should have so I googled as well and the site I landed on gave a different answer than the one you had.

To me the answers I've seen involve too much ambiguity:

Extreme spoiler, not my guess.......

Spoiler

This site says it's July 17th, not the 16th.

http://www.businessinsider.com/answe...problem-2015-4

[LowerWolf]

Re: Logic riddle gone viral (math-ish)

Your spoiler has the same date as the answer I found on google. I read the explanation, which makes sense, I guess. I need to think about it some more.

[kehlis]

Re: Logic riddle gone viral (math-ish)

Your spoiler has the same date as the answer I found on google. I read the explanation, which makes sense, I guess. I need to think about it some more.

Unless I'm missing something the day of your spoiler (in your first sentance) is one day off from the one in the link I posted.

[Blzer]

Re: Logic riddle gone viral (math-ish)

Great, I'm not getting too thrilled about running into an ambiguous answer haha!

[Brandwin]

Re: Logic riddle gone viral (math-ish)

Pretty sure I nailed it. This is how I got the answer...

Spoiler

[Phobia]

Re: Logic riddle gone viral (math-ish)

I won't even try, it just makes me feel stupid so I avoid the riddle and move on :wink:

[Blzer]

Re: Logic riddle gone viral (math-ish)

Okay, so I gave this problem to my Algebra 1 students. The great thing about this kind of problem is it doesn't take a math mind, but someone engaged in math might find the most intrigue out of it.

They were able to get more out of it than I was, and I think they solved it correctly. It's different than what you guys came up with, so I'll try and explain (to the best of my ability) what we got together, and how we came up with it:

Spoiler

First of all, I made the mistake of recursively applying the dialogue back-and-forth (meaning that I would use Albert's line about Bernard over and over again).

Secondly, it's important that we deduce Bernard only knows when Cheryl's birthday is after Albert says his line.

Thirdly, the most important part I was missing the first time... Albert isn't aware that Bernard doesn't know just because, but rather he finds out that Bernard doesn't know because of the information that he knows.

Anyway, the first stuff remains the same... it can't be May 19th or June 18th because if it was, then Bernard would know. Then it also can't be June 17th because if it was, then Albert would know (process of elimination).

Here's where things differ (this also could have applied for June), and this is the hardest part (mind you, my students figured this part out)... it can't be in May either. The bit of dialogue where Albert says that he knows Bernard doesn’t know means that he is only certain because it’s not May 19th or June 18th. If it was May 19th or June 18th, Bernard would know what it is of course. Albert is only certain that Bernard doesn’t know because if it was an 18 or 19, then he would know. Those two dates are only in May and June. This explanation is still iffy (it’s hard to word it), but it’s valid.

Next, Bernard says, “Aight, I didn’t know before, but now I’m certain.” This can only happen if he has a specific date in mind and he knows that Albert doesn’t know the answer yet. That means that we have to whittle this down to one specific month and date among the July’s and August’s. This takes out July 14th and August 14th, because if Bernard knew what it was he wouldn’t have this hang-up. Knowing that Albert still doesn’t know means it can’t be in August because there are still two dates, so it must be in July. This just leaves July 16th.

That's what we got, at least. I have not yet looked this up online or consulted it with anybody else. I thought those who were interested would see what we got and determine whether that sounds good or not.

[Antec]

Re: Logic riddle gone viral (math-ish)

Okay, so I gave this problem to my Algebra 1 students. The great thing about this kind of problem is it doesn't take a math mind, but someone engaged in math might find the most intrigue out of it.

They were able to get more out of it than I was, and I think they solved it correctly. It's different than what you guys came up with, so I'll try and explain (to the best of my ability) what we got together, and how we came up with it:

Spoiler

First of all, I made the mistake of recursively applying the dialogue back-and-forth (meaning that I would use Albert's line about Bernard over and over again).

Secondly, it's important that we deduce Bernard only knows when Cheryl's birthday is after Albert says his line.

Thirdly, the most important part I was missing the first time... Albert isn't aware that Bernard doesn't know just because, but rather he finds out that Bernard doesn't know because of the information that he knows.

Anyway, the first stuff remains the same... it can't be May 19th or June 18th because if it was, then Bernard would know. Then it also can't be June 17th because if it was, then Albert would know (process of elimination).

Here's where things differ (this also could have applied for June), and this is the hardest part (mind you, my students figured this part out)... it can't be in May either. The bit of dialogue where Albert says that he knows Bernard doesn’t know means that he is only certain because it’s not May 19th or June 18th. If it was May 19th or June 18th, Bernard would know what it is of course. Albert is only certain that Bernard doesn’t know because if it was an 18 or 19, then he would know. Those two dates are only in May and June. This explanation is still iffy (it’s hard to word it), but it’s valid.

Next, Bernard says, “Aight, I didn’t know before, but now I’m certain.” This can only happen if he has a specific date in mind and he knows that Albert doesn’t know the answer yet. That means that we have to whittle this down to one specific month and date among the July’s and August’s. This takes out July 14th and August 14th, because if Bernard knew what it was he wouldn’t have this hang-up. Knowing that Albert still doesn’t know means it can’t be in August because there are still two dates, so it must be in July. This just leaves July 16th.

That's what we got, at least. I have not yet looked this up online or consulted it with anybody else. I thought those who were interested would see what we got and determine whether that sounds good or not.

That's what I got. I'm positive it's the correct answer.

[Speedy]

Re: Logic riddle gone viral (math-ish)

Two things:

First, the error in the riddle that you folks are missing:

Spoiler

Bernard is not a college graduate; it's terrible syntax to state "At first, I don't know but then..." He should've said didn't as he was referring to his understanding in the past, not current time.

More to the point on the riddle:

Spoiler

Great riddle, Blzr...I spent way too long on this and eventually succumbed to temptation and googled the answer.

Good explanation:

http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/apr/13/how-to-solve-albert-bernard-and-cheryls-birthday-maths-problem

[Blzer]

Re: Logic riddle gone viral (math-ish)

I didn't like the way it was written either, but having heard this was from a competition in Singapore makes me wonder how well written the original question was in the first place. I tried to make it look exactly like the original so I wouldn't compromise any of the wording.

[Speedy]

Re: Logic riddle gone viral (math-ish)

It's very challenging and at least in your sector Blzr, really great thought regarding process chains in getting kids to understand cause-effect relationships on a substantially deeper level. Reminds me of my coding days.

This almost sounds like a riddle/question I would get in a Lean Six Sigma seminar with all the steps involved to derive to the answer.