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  • math riddles...

    Hello,

    I'm struggling with these math riddles (the solution for the first just seems so easy)

    1. A fictional city
    - no two inhabitants have the same number of hairs
    - no one has 302306 hairs
    - there is nobody with equal or more hairs than inhabitants
    - there are no 1000 people that have a birthday on the same day
    How many inhabitants can there be at most ?

    And for another riddle, I really have no clue (yet ?):
    2. Complete the sequence
    31 41 59 26 ??


    Any suggestions ?


    Jörg
    pixar
    Dream as if you'll live forever. Live as if you'll die tomorrow. (James Dean)

  • #2
    Ok, for the 1st riddle:

    Since there aren't 1000 people with the same birthday, 999*365 = 364,635 (max number of inhabitants)
    There is no inhabitant with 302306 hairs
    No inhabitant has a number of hairs > or = to the number of inhabitants.
    This means 364,635 - 1 (for the number 302,306) -1 (number 364,635 since nobody can have this amount of hair) + 1 (we have bald one !!!) = 364,634

    At least that's my guess

    Comment


    • #3
      1. 302306 ?

      Suppose every inhabitant is numbered by the amount of hairs he has. Start with inhabitant #1, and think of inhabitant # 302306 being the bald one. You can't have any more, because then you would end up with an inhabitant with the same number of hairs as there are inhabitants

      2. no clue
      Last edited by dZeus; 25 November 2002, 07:01.

      Comment


      • #4
        Originally posted by Dogbert
        Since there aren't 1000 people with the same birthday, 999*365 = 364,635 (max number of inhabitants)
        There is no inhabitant with 302306 hairs
        No inhabitant has a number of hairs > or = to the number of inhabitants.
        This means 364,635 - 1 (for the number 302,306) -1 (number 364,635 since nobody can have this amount of hair) + 1 (we have bald one !!!) = 364,634
        Yes, that is what I thought (but I used 999*366, as the question concerns a worst case scenario and a leap year has 366 days ).
        An additional question: does someone with 302307 hairs have 302306 hairs ? Dobert apparently chose "no", where dZeus chose "yes"... I would be tempted to choose no, again for having the worst case as high as possible.

        But the solution (in either case) is so simple, that I don't really trust it. (knowing where I got the question, they usually are much more difficult).

        Jörg
        pixar
        Dream as if you'll live forever. Live as if you'll die tomorrow. (James Dean)

        Comment


        • #5
          The second one appears to be the digits of pi.
          Blah blah blah nick blah blah confusion, blah blah blah blah frog.

          Comment


          • #6
            Originally posted by Ribbit
            The second one appears to be the digits of pi.
            Yes

            3.1 41 59 26 53 6. . .

            Comment


            • #7
              So searching for a pattern is not going to get you anywhere...

              3.1415926536 is all I can remember offhand (edit: except I think that the last digit is a rounding, so should be a "5"...).

              what about:

              271 828 182 845 ?
              DM says: Crunch with Matrox Users@ClimatePrediction.net

              Comment


              • #8
                Originally posted by Ribbit
                The second one appears to be the digits of pi.

                Great find ! In another question (concerning a circle and a rectangle) they mention that "as a reminder, pi=3.1415926535897....", but you don't need pi for that question. Guess this is their hint for the last question.

                GNEP: hehe....

                Jörg
                pixar
                Dream as if you'll live forever. Live as if you'll die tomorrow. (James Dean)

                Comment


                • #9
                  Originally posted by VJ
                  Yes, that is what I thought (but I used 999*366, as the question concerns a worst case scenario and a leap year has 366 days ).
                  An additional question: does someone with 302307 hairs have 302306 hairs ? Dobert apparently chose "no", where dZeus chose "yes"... I would be tempted to choose no, again for having the worst case as high as possible.

                  But the solution (in either case) is so simple, that I don't really trust it. (knowing where I got the question, they usually are much more difficult).

                  Jörg
                  I fail to grasp what you mean there... I didn't say that there can't be more than 302306 people because people with 302307 hairs also have 302306 hairs...
                  It would be quite safe to assume that they only prohibit people with the exact amount of 302306 hairs.
                  However, you can't have any more, because with every amount of inhabitants larger, you would end up with the 'last' inhabitant having at least the same amount of hairs as there are inhabitants.

                  (I hope this makes sense)
                  Last edited by dZeus; 25 November 2002, 07:19.

                  Comment


                  • #10
                    hmm, yes, it does make sense...
                    I see your point


                    Jörg
                    pixar
                    Dream as if you'll live forever. Live as if you'll die tomorrow. (James Dean)

                    Comment


                    • #11
                      Originally posted by GNEP
                      So searching for a pattern is not going to get you anywhere...

                      3.1415926536 is all I can remember offhand (edit: except I think that the last digit is a rounding, so should be a "5"...).

                      what about:

                      271 828 182 845 ?

                      e

                      Comment


                      • #12
                        e-yup!
                        DM says: Crunch with Matrox Users@ClimatePrediction.net

                        Comment


                        • #13
                          no matrox, no matroxusers.

                          Comment


                          • #14
                            for a minute I was rather intrigued with the notion of memorizing pi (must be my math/physics background), then I remembered - I HAVE A LIFE!
                            Yeah, well I'm gonna build my own lunar space lander! With blackjack aaaaannd Hookers! Actually, forget the space lander, and the blackjack. Ahhhh forget the whole thing!

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                            • #15
                              I have another one, but I need to cover one basic thing first:

                              1 divided by 3 is 0.33333 and endless 3s. What is the notation u use for infinitly repeating figures?

                              We use 0.3 with a forward slash through the 3 (but I can;t get that in this post). Can we agree 0.3/ means 1/3?

                              If so, prove 0.9/ equals one....
                              Umf
                              Join MURCs Distributed Computing effort for Rosetta@Home and help fight Alzheimers, Cancer, Mad Cow disease and rising oil prices.
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