# 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:** 10\ **Page:** 4
**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 19, 2013, 6:47pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/61 "2013-02-19T18:47:32Z")
Actually, I got your question correctly, but I messed up the names in my answer. Ben is given M Mark is given N The date is in the form M/N/70 Ben is the first to speak. You ask: > [@](#): > > I’m asking how Ben, not knowing what Mark was told, could possibly make the statement that he is certain Mark did not know the correct answer, before Mark even had the opportunity to answer Mr. Tau’s question! The only thing Ben can be certain of at the point he is asked is that HE does not know the answer. My answer should have read: > [@](#): > > Check again. Ben can be certain that Mark does not know the answer, since Ben was given a “9”. He can only make this statement truthfully if he was given a “3” or a “9.” The logic game is figuring out what Mark and Ben were given to make those logic statements truthful. ---
**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 19, 2013, 6:54pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/62 "2013-02-19T18:54:04Z")
> [@pulykamell](#): > > The date is in the form M/N/70 DAGNABBIT!!! I swear I am going to break something. N/M/70 ---
**Author:** ![worksheet](https://avatars.discourse-cdn.com/v4/letter/w/a587f6/32.png) [@worksheet](https://boards.straightdope.com/u/worksheet)\ **Post date:** [February 19, 2013, 7:06pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/63 "2013-02-19T19:06:39Z")
> [@pulykamell](#): > > And even that doesn’t work quite right. I don’t think Ben can truthfully guarantee that Mark doesn’t know the dates at that point. > > Sorry…my brain is starting to hurt. Next time, I promise to think things all the way out before I type them. But it doesn’t seem to me that your logic works, as 4/3 will have been eliminated by the statement assuring that Mark doesn’t know. Yea, so by backwards induction, only 4/3 is possible, which Mark proves to be the answer, as 4/3 is the only answer that is unique. If it is any other answer, Mark would not have said “now I know”. He would have agree that he “don’t know”. Ben is either trying to get more information out of Mark by that statement, or he simply make a mistake. 4/3 5/3 8/3 1/9 5/9 1/12 8/12 I would ultimately agree that this train of thought opens up more loophole than the conventional 1/9 ---
**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 19, 2013, 7:20pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/64 "2013-02-19T19:20:33Z")
I don’t follow the backwards induction to make 4/3 possible, to be honest. But no matter. I still think there is a big initial problem in the assumption that you can take Mark’s initial silence to be informative to Ben. To me, the logic of the puzzle maker is rather clear. Now, this being the SDMB, I understand the nickpickery to justify other answers and ways of solving the puzzle. And I do like that. Thinking outside the box, right? But I don’t think Mark’s silence gives us reliable information where we can take a different train of logic. It may, it may not. ---
**Author:** ![worksheet](https://avatars.discourse-cdn.com/v4/letter/w/a587f6/32.png) [@worksheet](https://boards.straightdope.com/u/worksheet)\ **Post date:** [February 19, 2013, 7:38pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/65 "2013-02-19T19:38:13Z")
> [@pulykamell](#): > > I don’t follow the backwards induction to make 4/3 possible, to be honest. But no matter. I still think there is a big initial problem in the assumption that you can take Mark’s initial silence to be informative to Ben. To me, the logic of the puzzle maker is rather clear. Now, this being the SDMB, I understand the nickpickery to justify other answers and ways of solving the puzzle. And I do like that. Thinking outside the box, right?Just for clarification, I got this question from a friend and that was how I solved it since the start. I googled to this pg and thats all, I have not been involved in SDMB at all before this. So I can say I have not been a SDMB nickpicker, (at least not yet? LOL) But I don’t think Mark’s silence gives us reliable information where we can take a different train of logic. It may, it may not.I agree on this, thats why I say that I ultimately agree that the 1/9 answer is the best answer, I just want to throw my logic out for tries and see the flaws. 🙂 ---
**Author:** ![Bootis](https://avatars.discourse-cdn.com/v4/letter/b/e8c25b/32.png) [@Bootis](https://boards.straightdope.com/u/Bootis)\ **Post date:** [February 19, 2013, 7:47pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/66 "2013-02-19T19:47:05Z")
the answer is 1/9/1970, and i don’t think there is even anything wrong or vague about the wording 1. Ben’s number can’t be a 6 or 12, because if it were, there could be a possibility Mark could have a 2 or 7, thus knowing the whole date. So Ben must have either a 3 or a 9 for him to be sure that Mark can’t know the whole date. 2. After hearing Ben’s comment, Mark now also knows that Ben doesn’t have a 6 or 9, so for Mark, using this new knowledge, to now know the whole date, his only possible numbers are: Mark CANT have a 5, because if he did, he still wouldn’t know the date, since it could be either 5/3/1970 or 5/9/1970 1. After Mark says “now I know”, Ben now can know Mark’s 3 possible numbers. The only way Ben could then reply “now I know too”, is if Ben’s number is 9. If Ben had 3, he knows it could be 4/3/1970, or 8/3/1970. But if Ben has 9, he knows it must be 1/9/1970. Therefore, Ben must have a 9, and the date can only be 1/9/1970 ---
**Author:** ![Hyeen24](https://avatars.discourse-cdn.com/v4/letter/h/3ab097/32.png) [@Hyeen24](https://boards.straightdope.com/u/Hyeen24)\ **Post date:** [February 21, 2013, 10:02am UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/67 "2013-02-21T10:02:49Z")
> [@Bootis](#): > > the answer is 1/9/1970, and i don’t think there is even anything wrong or vague about the wording > > 1. Ben’s number can’t be a 6 or 12, because if it were, there could be a possibility Mark could have a 2 or 7, thus knowing the whole date. So Ben must have either a 3 or a 9 for him to be sure that Mark can’t know the whole date. > > 2. After hearing Ben’s comment, Mark now also knows that Ben doesn’t have a 6 or 9, > so for Mark, using this new knowledge, to now know the whole date, his only possible numbers are: > > Mark CANT have a 5, because if he did, he still wouldn’t know the date, since it could be either 5/3/1970 or 5/9/1970 > > 1. After Mark says “now I know”, Ben now can know Mark’s 3 possible numbers. The only way Ben could then reply “now I know too”, is if Ben’s number is 9. If Ben had 3, he knows it could be 4/3/1970, or 8/3/1970. But if Ben has 9, he knows it must be 1/9/1970. > > Therefore, Ben must have a 9, and the date can only be 1/9/1970 Yes . My answer is the same . All other answer is wrong ---
**Author:** ![Mince](https://avatars.discourse-cdn.com/v4/letter/m/ecd19e/32.png) [@Mince](https://boards.straightdope.com/u/Mince)\ **Post date:** [February 21, 2013, 10:20am UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/68 "2013-02-21T10:20:18Z")
Insight? Yeah: if there’s no solution, then there’s no solution. I don’t know what the others in this thread are on about. ---
**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 21, 2013, 3:23pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/69 "2013-02-21T15:23:36Z")
> [@Mince](#): > > Insight? Yeah: if there’s no solution, then there’s no solution. I don’t know what the others in this thread are on about. In case this is serious, no solution was given to the problem on the webpage. There is a solution, and we all pretty much agree it’s 1/9/70. ---
**Author:** ![teddybound](https://avatars.discourse-cdn.com/v4/letter/t/8e7dd6/32.png) [@teddybound](https://boards.straightdope.com/u/teddybound)\ **Post date:** [February 22, 2013, 7:58pm UTC](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719/70 "2013-02-22T19:58:05Z")
In another forum, there’s an argument between the answers 1/9 and 4/3. [http://forums.hardwarezone.com.sg/eat-drink-man-woman-16/[help]-solve-question-4108755.html](http://forums.hardwarezone.com.sg/eat-drink-man-woman-16/%5Bhelp%5D-solve-question-4108755.html) Most people are convinced the answer is 1/9, but a few stubborn ones are arguing for 4/3, or even other answer. Please go take a look, and take a stand! 🙂 [Previous page](https://boards.straightdope.com/t/tough-puzzle-with-no-solution-any-insight/650719.md?page=3)