GUESS Birthday Quiz

[emoke05]

Ben and Mark are students of Mr Smith. Mr Smith's birthday is D/M/1970 and both of them know that Mr Smith's birthday is one of these 10 dates:

4/3/1970 5/3/1970 8/3/1970
4/6/1970 7/6/1970
1/9/1970 5/9/1970
1/12/1970 2/12/1970 8/12/1970

Mr Smith tells Ben the value of M and tell Mark the value of D. Then Mr Smith asks them: "Do you know when is my birthday?"

Ben says: "I don't know, but I can ensure that Mark doesn't know too."
Mark says: "Initially I don't know, but I know it now."
Ben says: "Oh, then I know it too."

Base on the dialogue and the dates given, can you figure out which date is Mr Smith's birthday?

PLEASE HELP!

 

[Deleted member 4993]

Ben and Mark are students of Mr Smith. Mr Smith's birthday is D/M/1970 and both of them know that Mr Smith's birthday is one of these 10 dates:4/3/1970 5/3/1970 8/3/19704/6/1970 7/6/1970 1/9/1970 5/9/19701/12/1970 2/12/1970 8/12/1970Mr Smith tells Ben the value of M and tell Mark the value of D. Then Mr Smith asks them: "Do you know when is my birthday?" Ben says: "I don't know, but I can ensure that Mark doesn't know too." Mark says: "Initially I don't know, but I know it now."Ben says: "Oh, then I know it too."Base on the dialogue and the dates given, can you figure out which date is Mr Smith's birthday? PLEASE HELP!

Does Ben know that he has been told the "value" of M?

Does Mark know that he has been told the "value" of D?

 

[soroban]

Hello, emoke05!

Ben and Mark are students of Mr. Smith.
Mr. Smith's birthday is \(\displaystyle D/M/1970\) and both of them know that
Mr. Smith's birthday is one of these 10 dates:

. . \(\displaystyle \begin{array}{ccccc}4/3 & 5/3 & 8/3 & 4/6 & 7/6 \\ 1/9 & 5/9& 1/12 & 2/12 & 8/12\end{array}\)

Mr. Smith tells Ben the value of \(\displaystyle M\) and tells Mark the value of \(\displaystyle D.\)
Then Mr. Smith asks them: "Do you know when is my birthday?"

Ben says: "I don't know, but I can ensure that Mark doesn't know too."
Mark says: "Initially I don't know, but I know it now."
Ben says: "Oh, then I know it too."

Based on the dialogue and the dates given,
can you figure out which date is Mr Smith's birthday?

Here are the possible birth dates:

. . \(\displaystyle \begin {array}{c}\text{Jan 9 }\;\text{ Jan 12} \\ \text{Feb 12} \\ \text{Apr 3 }\;\text{ Apr 6} \\ \text{May 3 }\;\text{ May 9} \\ \text{July 9} \\ \text{Aug 3 }\;\text{Aug 12} \end{array}\)


Ben knows the Month and Mark knows the Date.

Ben's first answer indicates that the birthday is not Feb.12 or July 6.

Then we have these possible dates:

. . \(\displaystyle \begin {array}{c}\text{Jan 9 }\;\text{ Jan 12} \\ \text{Apr 3 }\;\text{ Apr 6} \\ \text{May 3 }\;\text{ May 9} \\ \text{Aug 3 }\;\text{Aug 12} \end{array}\)

Mark knows the date of the birthday.
If the date were 3, 9, or 12, Mark still would not know the month.
Since he knew the birthday, it must have been the 6th.
The birthday was April 6.

Reasoning similarly, Ben would have concluded the same.

 

[JeffM]

I do not buy Soroban's answer because he has written down the July date incorrectly. In the original problem, it was the 6th. He has written down the 9th.

In Soroban's problem, the correct date is 4/6/70. But, as Soroban has written the problem, April is the only month where the 6th is feasible. So if Mark were given the 6th originally, he would have known the correct date regardless of Ben's answer. But that is not what the problem states.

I agree with Soroban's logic this far. Ben was not told July or February was the correct month because knowing the month in those cases was sufficient to identify the date. So we know that neither July 6 nor February 12 are the correct dates.

So that leaves as possible dates:

Jan 9 and 12

April 3 and 6

May 3 and 9

August 3 and 12

And it is true that Mark was not originally given enough information to solve the problem.

If Mark was told the 3rd, he would not have been able to distinguish among April, May, and August 3rd.
If told the 6th, he would not have been able to distinguish between April and July.
If told the 9th, he would not have been able to distinguish between January and May.
If told the 12th, he would not have been able to distinguish among January, February, and August.

The crux of the problem is this. Ben knows that the correct date is not July 6 and knows that Mark can deduce that from his answer. So Ben also knows that if the date given to Mark were the 6th, Mark could identify April 6th as Smith's birthday. But Ben says this is impossible. But the only way Ben can know that is if he also knows that the correct month is not April and so the date given cannot have been the 6th.

So that leaves as possibilities

Jan 9 and 12

May 3 and 9

August 3 and 12

I must admit I cannot get past this point. I am wondering if the problem was transcribed correctly.

If Mark was told the 3rd, he would not have been able to distinguish between May and August.
If told the 9th, he would not have been able to distinguish between January and May.
If told the 12th, he would not have been able to distinguish between January and August.

 

[lillybeth]

I figured it out! without anyone telling me the answer! p.s. I didn't look at other peoples answers yet!

April 6, cuz one of the kids knew the date, and the other one knew the month. So if the kid with the date said he knew the answer, then the answer is April 6th, cuz that is the only date with a 6. And then since the first kid said that he knew the answer, then the second kid knew the answer too, because of the above.

Sense of accomplishment.

 

[JeffM]

Will you guys please tell me where the heck you get your dates?

Dates are clearly:

Mar 4, 5 and 8

Jun 4 and 7

Sep 1 and 5

Dec 1, 2 and 8

Oh. The old "Americans write dates differently from everyone else" trap.

 

[Deleted member 4993]

Oh. The old "Americans write dates differently from everyone else" trap.

No trap...

The OP said:

Ben and Mark are students of Mr Smith. Mr Smith's birthday is D/M/1970 and both of them know that Mr Smith's birthday is one of these 10 dates:

 

[JeffM]

No trap...

The OP said:

Ben and Mark are students of Mr Smith. Mr Smith's birthday is D/M/1970 and both of them know that Mr Smith's birthday is one of these 10 dates:

I wasn't saying that the trap was set by the poster. Saying it was set by my own habits.

 

[JeffM]

Well Soroban and Jeff, yer still giving me headaches,
even if your dates were correct.

Denis, I doubt it would help your headache were I to explain why my reasoning would have been correct had the problem been as I misread it. Just the syntax of that sentence is giving ME a headache. I think I got a pluperfect subjunctive in there.

 

[JeffM]

Hmmm...looked at it again...think I got it...(I did say 99% sure, not 100%!)

Puzzle would be somewhat clearer if worded this way:

Ben and Mark are students of Mr Smith. Mr Smith tells them:
my birthday is in 1970, on one of these 10 days:
Mar 4 ; Mar 5 ; Mar 8
Jun 4 ; Jun 7
Sep 1 ; Sep 5
Dec 1 ; Dec 2 ; Dec 8

Mr Smith tells Ben the month, and tells Mark the day.
Then Mr Smith asks them: "Do you know when my birthday is?"

Mark says: "I don't know"
Ben says: "I knew that you didn't know"
Mark says: "Now I know"
Ben says: "Ah, now I also know"

Base on above dialogue and dates, figure out Mr Smith's birthday?
*************************************************

So we have these dates:
Mar 4
Mar 5
Mar 8

Jun 4
Jun 7 (7 is unique)

Sep 1
Sep 5

Dec 1
Dec 2 (2 is unique)
Dec 8

Sure no fun trying to "explain", but here goes:

Since Mark first says he doesn't know, then Mark did not get
7 or 2; so Mark got 1 or 4 or 5 or 8.

Since Ben replies that he already knew Mark didn't know, then
Ben got Mar or Sep: else he wouldn't be sure Mark didn't know.

So we assume MarkFL(?!) is smart enough to now realise month is
Mar or Sep; so day cannot be 5, since it appears in both months
So we are now left with:
Mar 4
Mar 8
Sep 1
meaning that Mark got 1 or 4 or 8.

For the clincher:
Mark got 1, so date is Sep 1.
Why not 4 or 8? He'd know month was Mar then...
BUT Ben wouldn't know, since if he had Mar, he'd have 2 choices.
So since Ben also knows, he MUST have had Sep.

Hank you, Hank you ... I'm leaving the building...:grin:

This puzzle is horribly worded. Perhaps we did not get the original wording.

Anyway, as the puzzle was given to us, Ben speaks first, and Ben is the guy who knows the month. (This is silly. Mark should be the guy who knows the month and Dave should be the guy who knows the day.) So denis's logic cannot be exactly right because he has Mark speaking first. (I seem to be not alone in having trouble reading this week.) But the fundamental question is whether denis got the correct answer. He did.

Ben says "I don't know the date with certainty, but I do know with certainty that Mark could not have answered with certainty if you had asked him first." That is not how the puzzle is worded, but I think it is what is meant.

Now Mark could have answered correctly with certainty if Mark had been told that the day of the month was 2 or 7 because each of those days occurs in only one month, namely December and June respectively. So Ben could have been certain about Mark's initial inability to answer with certainty only if the month told to Ben was March or September because each day in either of those months is duplicated in at least one other month.

So Mark now knows that the month is September or March.

So the possible dates are now

March 4, 5, and 8 and September 1 and 5.

If Mark was given 5 as the day, he still would not know the birthdate after Ben's compound answer, but he does know so 5 is not the date.

That leaves as possible dates

March 4 and 8 and September 1.

So the day identifies the month, and Mark knows now with certainty and so states that his knowledge is now certain.

Based on that comment, Ben can figure out that 5 is not the date.

If Ben had been told March, Ben still could not know the date with certainty because there are two possible days in March. But he does know the date, so he was not told March. He must have been told September.

September 1.