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RE: [PrimeNumbers] A game

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  • Jon Perry
    ... 29 = 4.7+1, and 7 is prime 5.29 = 145 = 1mod4 so your move is not legal. ... I will assume that you misunderstood the rules, and allow you another chance.
    Message 1 of 28 , Sep 4, 2002
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      >If k is prime or 1, then the next person must respond with a prime q such
      >that pq=-1mod4

      29 = 4.7+1, and 7 is prime

      5.29 = 145 = 1mod4

      so your move is not legal.

      >This game is very intolerant - a false move results in immediate expulsion
      >from the game.

      I will assume that you misunderstood the rules, and allow you another
      chance.

      Jon Perry
      perry@...
      http://www.users.globalnet.co.uk/~perry/maths
      BrainBench MVP for HTML and JavaScript
      http://www.brainbench.com
    • jbrennen
      ... Jon, I analyzed your game, and you should note that in a 2-player game, an opening move of 29 is a losing move. After a 29, these are all winning moves for
      Message 2 of 28 , Sep 4, 2002
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        --- In primenumbers@y..., "Jon Perry" <perry@g...> wrote:
        >
        > 29
        >

        Jon, I analyzed your game, and you should note that in a 2-player
        game, an opening move of 29 is a losing move.

        After a 29, these are all winning moves for the second player:

        23, 31, 47, 59, 71, 79, 83

        (any prime of the form 4k-1 with k composite)

        So if you want to play...

        29 -> 23 -> your turn...
      • Jon Perry
        Hmmm... deep thought involved: 29 - 23 - 3 23=4.6-1, 6 is composite, therefore 23.3 must be 1mod4 (1 is prime) Jon Perry perry@globalnet.co.uk
        Message 3 of 28 , Sep 4, 2002
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          Hmmm... deep thought involved:

          29 -> 23 -> 3

          23=4.6-1, 6 is composite, therefore 23.3 must be 1mod4

          (1 is prime)

          Jon Perry
          perry@...
          http://www.users.globalnet.co.uk/~perry/maths
          BrainBench MVP for HTML and JavaScript
          http://www.brainbench.com
        • jbrennen
          ... To which I respond: 29 - 23 - 3 - 5
          Message 4 of 28 , Sep 4, 2002
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            --- In primenumbers@y..., "Jon Perry" <perry@g...> wrote:

            > 29 -> 23 -> 3

            To which I respond:

            29 -> 23 -> 3 -> 5
          • Jon Perry
            ##To which I respond: ##29 - 23 - 3 - 5 29 - 23 - 3 - 5 - 83 (p.s. post to the list, as anyone can join it at any time, thus smashing your I m going to
            Message 5 of 28 , Sep 5, 2002
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              ##To which I respond:

              ##29 -> 23 -> 3 -> 5

              29 -> 23 -> 3 -> 5 -> 83

              (p.s. post to the list, as anyone can join it at any time, thus smashing
              your 'I'm going to win 'coz I went second' into unimaginably little pieces)

              Jon Perry
              perry@...
              http://www.users.globalnet.co.uk/~perry/maths
              BrainBench MVP for HTML and JavaScript
              http://www.brainbench.com


              -----Original Message-----
              From: jbrennen [mailto:jack@...]
              Sent: 04 September 2002 21:38
              To: primenumbers@yahoogroups.com
              Subject: [PrimeNumbers] Re: A game


              --- In primenumbers@y..., "Jon Perry" <perry@g...> wrote:

              > 29 -> 23 -> 3
            • jbrennen
              ... First, 29 - 23 - 3 - 5 - 83 - 31 Second, that s not what I said... What I said was that *in a two player game*, 29 is a losing play to start the game.
              Message 6 of 28 , Sep 5, 2002
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                --- In primenumbers@y..., "Jon Perry" <perry@g...> wrote:
                >
                > 29 -> 23 -> 3 -> 5 -> 83
                >
                > (p.s. post to the list, as anyone can join it at any time, thus
                > smashing your 'I'm going to win 'coz I went second' into
                > unimaginably little pieces)

                First,

                29 -> 23 -> 3 -> 5 -> 83 -> 31

                Second, that's not what I said...
                What I said was that *in a two player game*, 29 is a losing
                play to start the game. Note that any prime of the form 4k+/-1
                with k composite is a winning opening (the smallest such number
                being 17). All other openings are losing openings.

                Third, if anyone can join at any time, the concept of winning or
                losing is nonsensical. Is the 'winner' the last person able to
                add a number? If so, it's just a race to see who can post first
                after the penultimate number is posted. And there is no 'loser'
                of course, since nobody is obligated to 'go next' ...


                The following applies to the 2-player game only...


                Note that the opening strategy varies depending on the upper limit
                of primes we're allowed to use.

                A = 4k-1, where k is 1 or prime
                B = 4k+1, where k is composite
                C = 4k+1, where k is 1 or prime
                D = 4k-1, where k is composite

                Prime limit: winning play to start

                3: A
                5: any opening loses
                7: A
                11: A
                13: A
                17: B or C
                19: B or C
                23: B or D
                29: B or D
                31: B or C
                37: A
                41: B or C
                43: B or C
                47: B or D
                53: B or D
                59: B or C
                61: A
                67: A
                71: A
                73: B or D
                79: B or C
                83: B or D
                89: A
                97: B or D

                An obvious question -- is limit=5 the only game for which the
                opening player has no forced win?
              • jbrennen
                ... I just answered this for myself... If the limit is 389, the opening player has no winning play.
                Message 7 of 28 , Sep 5, 2002
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                  --- In primenumbers@y..., "jbrennen" <jack@b...> wrote:
                  >
                  > An obvious question -- is limit=5 the only game for which the
                  > opening player has no forced win?

                  I just answered this for myself...

                  If the limit is 389, the opening player has no winning play.
                • Jon Perry
                  29 - 23 - 3 - 5 - 83 - 31 - 7 Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths BrainBench MVP for HTML and JavaScript
                  Message 8 of 28 , Sep 6, 2002
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                    29 -> 23 -> 3 -> 5 -> 83 -> 31 -> 7

                    Jon Perry
                    perry@...
                    http://www.users.globalnet.co.uk/~perry/maths
                    BrainBench MVP for HTML and JavaScript
                    http://www.brainbench.com
                  • jbrennen
                    29 - 23 - 3 - 5 - 83 - 31 - 7 - 13
                    Message 9 of 28 , Sep 6, 2002
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                      29 -> 23 -> 3 -> 5 -> 83 -> 31 -> 7 -> 13
                    • Jon Perry
                      29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 97 (imagine this was a C++ object!) Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths
                      Message 10 of 28 , Sep 6, 2002
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                        29 -> 23 -> 3 -> 5 -> 83 -> 31 -> 7 -> 13 -> 97

                        (imagine this was a C++ object!)

                        Jon Perry
                        perry@...
                        http://www.users.globalnet.co.uk/~perry/maths
                        BrainBench MVP for HTML and JavaScript
                        http://www.brainbench.com
                      • jbrennen
                        ... A problem -- 97 is not a valid successor to 13. 13 is of the form 4k+1, with k prime, so you must respond with a prime q such that 13q = -1 (mod 4).
                        Message 11 of 28 , Sep 6, 2002
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                          --- In primenumbers@y..., "Jon Perry" <perry@g...> wrote:

                          > 29 -> 23 -> 3 -> 5 -> 83 -> 31 -> 7 -> 13 -> 97

                          A problem -- 97 is not a valid successor to 13.

                          13 is of the form 4k+1, with k prime, so you must respond
                          with a prime q such that 13q = -1 (mod 4).
                        • Jon Perry
                          Sorry - I must have been sleep surfing. ... Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths BrainBench MVP for HTML and
                          Message 12 of 28 , Sep 7, 2002
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                            Sorry - I must have been sleep surfing.

                            > 29 -> 23 -> 3 -> 5 -> 83 -> 31 -> 7 -> 13 -> 79

                            Jon Perry
                            perry@...
                            http://www.users.globalnet.co.uk/~perry/maths
                            BrainBench MVP for HTML and JavaScript
                            http://www.brainbench.com


                            -----Original Message-----
                            From: jbrennen [mailto:jack@...]
                            Sent: 06 September 2002 22:05
                            To: primenumbers@yahoogroups.com
                            Subject: [PrimeNumbers] Re: A game


                            --- In primenumbers@y..., "Jon Perry" <perry@g...> wrote:

                            > 29 -> 23 -> 3 -> 5 -> 83 -> 31 -> 7 -> 13 -> 97

                            A problem -- 97 is not a valid successor to 13.

                            13 is of the form 4k+1, with k prime, so you must respond
                            with a prime q such that 13q = -1 (mod 4).





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                          • jbrennen
                            29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47
                            Message 13 of 28 , Sep 9, 2002
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                              29 -> 23 -> 3 -> 5 -> 83 -> 31 -> 7 -> 13 -> 79 -> 47
                            • Jon Perry
                              29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths BrainBench MVP for
                              Message 14 of 28 , Sep 9, 2002
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                                29 -> 23 -> 3 -> 5 -> 83 ->
                                31 -> 7 -> 13 -> 79 -> 47 ->
                                11

                                Jon Perry
                                perry@...
                                http://www.users.globalnet.co.uk/~perry/maths
                                BrainBench MVP for HTML and JavaScript
                                http://www.brainbench.com
                              • jbrennen
                                29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53
                                Message 15 of 28 , Sep 9, 2002
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                                  29 -> 23 -> 3 -> 5 -> 83 ->
                                  31 -> 7 -> 13 -> 79 -> 47 ->
                                  11 -> 53
                                • Jon Perry
                                  29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53 - 19 Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths
                                  Message 16 of 28 , Sep 9, 2002
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                                    29 -> 23 -> 3 -> 5 -> 83 ->
                                    31 -> 7 -> 13 -> 79 -> 47 ->
                                    11 -> 53 -> 19

                                    Jon Perry
                                    perry@...
                                    http://www.users.globalnet.co.uk/~perry/maths
                                    BrainBench MVP for HTML and JavaScript
                                    http://www.brainbench.com
                                  • jbrennen
                                    29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53 - 19 - 17
                                    Message 17 of 28 , Sep 9, 2002
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                                      29 -> 23 -> 3 -> 5 -> 83 ->
                                      31 -> 7 -> 13 -> 79 -> 47 ->
                                      11 -> 53 -> 19 -> 17
                                    • Jon Perry
                                      29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53 - 19 - 17 - 97 Jon Perry perry@globalnet.co.uk
                                      Message 18 of 28 , Sep 10, 2002
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                                        29 -> 23 -> 3 -> 5 -> 83 ->
                                        31 -> 7 -> 13 -> 79 -> 47 ->
                                        11 -> 53 -> 19 -> 17 -> 97

                                        Jon Perry
                                        perry@...
                                        http://www.users.globalnet.co.uk/~perry/maths
                                        BrainBench MVP for HTML and JavaScript
                                        http://www.brainbench.com
                                      • jbrennen
                                        29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53 - 19 - 17 - 97 - 37
                                        Message 19 of 28 , Sep 10, 2002
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                                          29 -> 23 -> 3 -> 5 -> 83 ->
                                          31 -> 7 -> 13 -> 79 -> 47 ->
                                          11 -> 53 -> 19 -> 17 -> 97 ->
                                          37
                                        • Jon Perry
                                          29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53 - 19 - 17 - 97 - 37 - 61 Jon Perry perry@globalnet.co.uk
                                          Message 20 of 28 , Sep 11, 2002
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                                            29 -> 23 -> 3 -> 5 -> 83 ->
                                            31 -> 7 -> 13 -> 79 -> 47 ->
                                            11 -> 53 -> 19 -> 17 -> 97 ->
                                            37 -> 61

                                            Jon Perry
                                            perry@...
                                            http://www.users.globalnet.co.uk/~perry/maths
                                            BrainBench MVP for HTML and JavaScript
                                            http://www.brainbench.com
                                          • jbrennen
                                            29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53 - 19 - 17 - 97 - 37 - 61 - 41
                                            Message 21 of 28 , Sep 11, 2002
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                                              29 -> 23 -> 3 -> 5 -> 83 ->
                                              31 -> 7 -> 13 -> 79 -> 47 ->
                                              11 -> 53 -> 19 -> 17 -> 97 ->
                                              37 -> 61 -> 41
                                            • Jon Perry
                                              29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53 - 19 - 17 - 97 - 37 - 61 - 41 - 73 Jon Perry perry@globalnet.co.uk
                                              Message 22 of 28 , Sep 11, 2002
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                                                29 -> 23 -> 3 -> 5 -> 83 ->
                                                31 -> 7 -> 13 -> 79 -> 47 ->
                                                11 -> 53 -> 19 -> 17 -> 97 ->
                                                37 -> 61 -> 41 -> 73

                                                Jon Perry
                                                perry@...
                                                http://www.users.globalnet.co.uk/~perry/maths
                                                BrainBench MVP for HTML and JavaScript
                                                http://www.brainbench.com
                                              • jbrennen
                                                29 - 23 - 3 - 5 - 83 - 31 - 7 - 13 - 79 - 47 - 11 - 53 - 19 - 17 - 97 - 37 - 61 - 41 - 73 - 89 Checkmate.
                                                Message 23 of 28 , Sep 11, 2002
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                                                  29 -> 23 -> 3 -> 5 -> 83 ->
                                                  31 -> 7 -> 13 -> 79 -> 47 ->
                                                  11 -> 53 -> 19 -> 17 -> 97 ->
                                                  37 -> 61 -> 41 -> 73 -> 89

                                                  Checkmate.
                                                • Jon Perry
                                                  Jack is hereby declared the Winner. How about we go again? - only this time if the k is prime, then the mod must be opposite to the last mod, otherwise the
                                                  Message 24 of 28 , Sep 11, 2002
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                                                    Jack is hereby declared the Winner.

                                                    How about we go again? - only this time if the k is prime, then the mod must
                                                    be opposite to the last mod, otherwise the same.

                                                    e.g. 13 -> (anything, say...) 17 ->

                                                    17 is 4.4+1, 4 is composite, therefore reply with a number that when
                                                    multiplied by 17 is the same sign as 13*17 (=1mod4), i.e. reply with a
                                                    1mod4.

                                                    If the second go was 19, then 13.19=3mod4, therefore as the k for 19 is 5,
                                                    reply wioth a 1mod4.

                                                    Jon Perry
                                                    perry@...
                                                    http://www.users.globalnet.co.uk/~perry/maths
                                                    BrainBench MVP for HTML and JavaScript
                                                    http://www.brainbench.com


                                                    -----Original Message-----
                                                    From: jbrennen [mailto:jack@...]
                                                    Sent: 11 September 2002 19:27
                                                    To: primenumbers@yahoogroups.com
                                                    Subject: [PrimeNumbers] Re: A game


                                                    29 -> 23 -> 3 -> 5 -> 83 ->
                                                    31 -> 7 -> 13 -> 79 -> 47 ->
                                                    11 -> 53 -> 19 -> 17 -> 97 ->
                                                    37 -> 61 -> 41 -> 73 -> 89

                                                    Checkmate.




                                                    Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
                                                    The Prime Pages : http://www.primepages.org



                                                    Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
                                                  • Jon Perry
                                                    I forgot to go first: 89 Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths BrainBench MVP for HTML and JavaScript
                                                    Message 25 of 28 , Sep 11, 2002
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                                                      I forgot to go first:

                                                      89

                                                      Jon Perry
                                                      perry@...
                                                      http://www.users.globalnet.co.uk/~perry/maths
                                                      BrainBench MVP for HTML and JavaScript
                                                      http://www.brainbench.com
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