# Tough puzzle with no solution.. any insight? **URL:** \ **Category:** The Game Room\ **Created:** [February 18, 2013, 5:55pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719 "2013-02-18T17:55:52Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![teddybound](https://avatars.discourse-cdn.com/v4/letter/t/8e7dd6/32.png) [@teddybound](https://boards.straightdope.com/u/teddybound)\ **Post date:** [February 18, 2013, 5:55pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/1 "2013-02-18T17:55:52Z")
Warning: I do not have the answer to this question! Anyone can help me break the code? [![](https://i.imgur.com/4yY0egz.jpg) ](https://i.imgur.com/4yY0egz.jpg) How do you embed the image?? ---
**Author:** ![Colibri](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/colibri/32/1841_2.png) [@Colibri](https://boards.straightdope.com/u/Colibri)\ **Post date:** [February 18, 2013, 6:05pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/2 "2013-02-18T18:05:12Z")
Moved to the Game Room. Colibri General Questions Moderator ---
**Author:** ![Zapp\_S](https://avatars.discourse-cdn.com/v4/letter/z/ee59a6/32.png) [@Zapp\_S](https://boards.straightdope.com/u/Zapp_S)\ **Post date:** [February 18, 2013, 6:17pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/3 "2013-02-18T18:17:42Z")
that’s gotta be 5/9/1970 my explanation is this: Ben says: “Mark doesn’t know too”. He doesn’t mean “too”, but “two”. What he means by that is that Mark’s number is not two nor divisible by two. He knows that because his number is 9, and no date with M=9 has first number N divisible by two. Then Mark responds by “initially I don’t know”, where by “initially” he means number one, thus the only remaining number N is 5. Ben now knows too. ---
**Author:** ![Evil\_Economist](https://avatars.discourse-cdn.com/v4/letter/e/c89c15/32.png) [@Evil\_Economist](https://boards.straightdope.com/u/Evil_Economist)\ **Post date:** [February 18, 2013, 6:21pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/4 "2013-02-18T18:21:32Z")
I’m going to guess that’s it’s 1/9/1970, though the wording is so bad it’s hard to be sure. Ben by himself can’t know the full date; any number Tan gives him would result in at least 2 choices: there are 3 each of xx/3/xxxx and xx/12/xxxx and 2 each of xx/6/xxxx and xx/9/xxxx. If Mark doesn’t know the full date then we know it’s not 7/xx/xxxx or 2/xx/xxxx (because if Mark had been given a 2 or a 7 then he would know the full date immediately). Ben says that he can ensure that Mark doesn’t know. That means he couldn’t have been given a xx/6/xxxx or xx/12/xxxx (because if he had been given one of those dates, there’s a chance Mark could have been given 7/xx/xxxx or 2/xx/xxxx). That means he must have been given xx/3/xxxx or xx/9/xxxx. If Mark now knows, that means he must have been given 1/xx/xxxx, 4/xx/xxxx, or 8/xx/xxxx (becasue if he had been given 5/xx/xxxx, there would still be ambiguity). Now Ben knows, so it must be 1/9/xxxx, because otherwise he still wouldn’t know (if it was xx/3/xxxx, he would be stuck between 4/3/xxxx 8/3/xxxx) ---
**Author:** ![Zapp\_S](https://avatars.discourse-cdn.com/v4/letter/z/ee59a6/32.png) [@Zapp\_S](https://boards.straightdope.com/u/Zapp_S)\ **Post date:** [February 18, 2013, 6:35pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/5 "2013-02-18T18:35:01Z")
That’s a much better answer than mine lol, but hey, I failed maths so what would I know ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [February 18, 2013, 6:55pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/6 "2013-02-18T18:55:32Z")
I’m not going to look at the other answers. Let’s follow the logic train here. Ben knows M. Mark knows N. The dates are conveniently arranged for us us that each row has the same M. Ben can only know the date if he is given a unique M. There are no unique Ms. Mark can only know the date if he is given a unique N. There are two unique Ns: 7 and 2. Since Ben can ensure that Mark doesn’t know, we know Mark can’t have any M that corresponds to the unique Ns. So, that eliminates: 4/6/1970, 7/6/1970, 1/12/1970, 2/12/1970, and 8/12/1970 We are left with: 4/3/70 5/3/70, 8/3/70 1/9/70, 5/9/70 So Mark either has 1, 4, 5, or 8. If Mark holds a 1, he knows it’s 1/9/70. If he holds a 4, it’s 4/3/70. If he holds an 8, it’s 8/3/70. If he holds a 5, there is not enough info, so it can’t be 5. We’re left with: 4/3/70, 8/3/70 1/9/70 Now, knowing this, Ben must be holding a 9, as if he is holding a 3, there is not enough information. So 1/9/70 ---
**Author:** ![robardin](https://avatars.discourse-cdn.com/v4/letter/r/43a26b/32.png) [@robardin](https://boards.straightdope.com/u/robardin)\ **Post date:** [February 18, 2013, 6:56pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/7 "2013-02-18T18:56:26Z")
It’s not a guess - it’s definitely 1/9. The birthday is N/M/1970. Ben is told M, Mark is told N. The possible dates given as N/M (all in 1970): 4/3, 5/3, 8/3 4/6, 7/6 1/9, 5/9 1/12, 2/12, 8/12 Sorted values of N = { 1, 1, 2, 4, 4, 5, 5, 7, 8, 8 } Sorted values of M = { 3, 3, 3, 6, 6, 9, 9, 12, 12, 12 } There is only one date with N=2 (2/12), and only one date with N=7 (7/6). If Mark knew N was either value, he would know the birthday without knowing M. Since Ben knows that Mark cannot know this, and Ben knows only M, that means M is neither 12 nor 6 (i.e., he knows for sure that there is no way that the birthday is either 2/12 or 7/6). The possible birthdays are now: 4/3, 5/3, 8/3 1/9, 5/9 Possible values of N = {1, 4, 5, 5, 8} Possible values of M = {3, 3, 3, 9, 9} With this narrowing down, Mark (who knows N) now knows the birthday - so it’s the one from this list with a unique value of N, which is 1. The birthday is 1/9. ---
**Author:** ![Baal\_Houtham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/baal_houtham/32/13604_2.png) [@Baal\_Houtham](https://boards.straightdope.com/u/Baal_Houtham)\ **Post date:** [February 18, 2013, 7:12pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/8 "2013-02-18T19:12:46Z")
I got 4-6. The month guy, Ben, didn’t know at first, which indicates a month with multiple possible days. That eliminates Feb, May, and July. Ben also says that the day guy, Mark, couldn’t know either. That eliminates the one-of-a-kind days: 9. Since with Ben’s volunteered info Mark now knows the date it means it’s the only unique number left: April 6. aka 4-6. ---
**Author:** ![Leaper](https://avatars.discourse-cdn.com/v4/letter/l/4bbf92/32.png) [@Leaper](https://boards.straightdope.com/u/Leaper)\ **Post date:** [February 18, 2013, 7:17pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/9 "2013-02-18T19:17:43Z")
> [@Baal\_Houtham](#): > > Ben also says that the day guy, Mark, couldn’t know either. That eliminates the one-of-a-kind days: 9. But 9 isn’t a one of a kind day. There’s 1/9 and 5/9. ---
**Author:** ![Baal\_Houtham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/baal_houtham/32/13604_2.png) [@Baal\_Houtham](https://boards.straightdope.com/u/Baal_Houtham)\ **Post date:** [February 18, 2013, 7:17pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/10 "2013-02-18T19:17:59Z")
> [@Baal\_Houtham](#): > > I got 4-6. Nevermind. I accidentally left out one of the possibilities (5-9) while doing my calculations. ---
**Author:** ![Zapp\_S](https://avatars.discourse-cdn.com/v4/letter/z/ee59a6/32.png) [@Zapp\_S](https://boards.straightdope.com/u/Zapp_S)\ **Post date:** [February 18, 2013, 7:22pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/11 "2013-02-18T19:22:05Z")
Whatever the answer is, you guys must agree that these Mark and Ben’s gotta be some damn mathematical geniuses if they can make up such mathematical calculations during a casual conversation ---
**Author:** ![Gary\_Robson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/gary_robson/32/3448_2.png) [@Gary\_Robson](https://boards.straightdope.com/u/Gary_Robson)\ **Post date:** [February 18, 2013, 7:33pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/12 "2013-02-18T19:33:24Z")
> [@teddybound](#): > > How do you embed the image?? You can’t. The only forum on the SDMB that allows embedded images in the Marketplace. ---
**Author:** ![Zapp\_S](https://avatars.discourse-cdn.com/v4/letter/z/ee59a6/32.png) [@Zapp\_S](https://boards.straightdope.com/u/Zapp_S)\ **Post date:** [February 18, 2013, 7:38pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/13 "2013-02-18T19:38:16Z")
Or as I think about it, by their manner of speaking maybe both Mark and Ben are stoned, along with Mr Tan, and the correct answer to the question “Base of the dialogue and the dates given, can you figure out which date is Mr Tan’s birthday?” is “nope”. ---
**Author:** ![Evil\_Economist](https://avatars.discourse-cdn.com/v4/letter/e/c89c15/32.png) [@Evil\_Economist](https://boards.straightdope.com/u/Evil_Economist)\ **Post date:** [February 18, 2013, 7:43pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/14 "2013-02-18T19:43:16Z")
> [@robardin](#): > > Possible values of N = {1, 4, 5, 5, 8} > Possible values of M = {3, 3, 3, 9, 9} > > With this narrowing down, Mark (who knows N) now knows the birthday - so it’s the one from this list with a unique value of N, which is 1. > > The birthday is 1/9. Aren’t 4 and 8 also unique values of N? ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [February 18, 2013, 7:48pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/15 "2013-02-18T19:48:21Z")
> [@Evil\_Economist](#): > > Aren’t 4 and 8 also unique values of N? Yeah, I’m not 100% sure on how **robardin** ’s explanation works (I’ve never been particularly good with sets), but I’m certain the three of us all got the right answer with 1/9/70. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [February 18, 2013, 7:51pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/16 "2013-02-18T19:51:55Z")
> [@Baal\_Houtham](#): > > I got 4-6. > > The month guy, Ben, didn’t know at first, which indicates a month with multiple possible days. That eliminates Feb, May, and July. We actually don’t know whether Ben is “the month guy” or “the day guy.” But it doesn’t matter. We know he’s the middle number guy and the dates are in the form N/M/1970. Ben is the M. Mark is the N. ---
**Author:** ![Evil\_Economist](https://avatars.discourse-cdn.com/v4/letter/e/c89c15/32.png) [@Evil\_Economist](https://boards.straightdope.com/u/Evil_Economist)\ **Post date:** [February 18, 2013, 8:14pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/17 "2013-02-18T20:14:37Z")
Let me think about this… ---
**Author:** ![Evil\_Economist](https://avatars.discourse-cdn.com/v4/letter/e/c89c15/32.png) [@Evil\_Economist](https://boards.straightdope.com/u/Evil_Economist)\ **Post date:** [February 18, 2013, 8:19pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/18 "2013-02-18T20:19:47Z")
OK, if we all agree on the answer, let’s consider variations. Same setup, but the conversation goes as follows: Bill says “I don’t know” Mark says, “I don’t know either” Bill says “Yeah, it’s a mystery” Mark says “Ha! You gave it away” ---
**Author:** ![robardin](https://avatars.discourse-cdn.com/v4/letter/r/43a26b/32.png) [@robardin](https://boards.straightdope.com/u/robardin)\ **Post date:** [February 18, 2013, 8:26pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/19 "2013-02-18T20:26:41Z")
> [@pulykamell](#): > > Yeah, I’m not 100% sure on how **robardin** ’s explanation works (I’ve never been particularly good with sets), but I’m certain the three of us all got the right answer with 1/9/70. Oops, I left out documenting a mental step that matches what you wrote, **pulykamell** : N/M could be 1/9, 4/3 or 8/3, but because Mark (the N guy) knows that Ben (the M guy) can figure out the date based on the restricted information, it means it’s the only date with a unique value of M. Let me try to rewrite it more clearly… It seems to me the stated problem is not clear on exactly when who knows what about who knows what. ---
**Author:** ![drewtwo99](https://avatars.discourse-cdn.com/v4/letter/d/d07c76/32.png) [@drewtwo99](https://boards.straightdope.com/u/drewtwo99)\ **Post date:** [February 18, 2013, 10:00pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/20 "2013-02-18T22:00:13Z")
These sorts of riddles only work if you preface them with, “Assume everyone involved is a perfect logician.” Anytime someone figures something out by a lack of information, or someone else not knowing the answer to something, the riddle of “how did he solve it?” only works if you assume the necessary players are perfect logicians. Otherwise I could just answer the riddle by saying, “Neither of them knew; they were just being wise asses,” and I’d be perfectly correct. [Next page](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719.md?page=2)