[pbmserv] Broadcast from jjartus via PBM Server

[pbmserv <pbmserv@gamerz.net>]

 Dear gamers,

 I wish to suggest a game of Nim (picking) type, from which it seems
 we don't have any. I have played it several times on a physical
 board. It is fast, can be played in some 10 minutes. It has simple
 rules, but is very complex. Up to the lasts moves is very difficult
 to see a winner, and it requires pattern and parity changing
 analysis. Moreover it should be very easy to program.

  I call it TriNim. It is played by 2 players on a Hex board, in a 5
  sided  triangle (15 cells) with that shape:

                  .
                 . .
                . . .
               . . . .
              . . . . .



  It can be set up in a Zertz board. The board is filled at random
  with 15 balls of three colors, 5 each, (gray, black and white).

  Players  alternate  moves  picking any number of balls from 1 to 5
  each  move,  regardless of color. The balls must be contiguous (no
  empty spaces) in a straight line in any direction or position. The
  game  ends  when  all  the  balls  have  been  picked.  Picking is
  compulsory (no "pass").

  The  aim is to "get a color". Getting a color means to have at the
  end  of  the  game an even number of balls of that color (0, 2, or
  4).  The  player that gets more colors (2 or 3) wins (against 1 or
  0, respectively).

  The maximum duration is then 15 moves, but often there are not
  more than 6 or 7. For simple patterns in the lasts moves it is
  easy to see a winning strategy, but complexity increases quickly
  with more balls.

  Anyone would like and be able to program it into the server?

  Then a different question arises: How many non equivalent starting
  configurations  are possible? Configurations related by a symmetry
  plane,  ternary  rotating  axis  of  symmetry or exchanging 2 or 3
  colors are equivalent. Any computer expert can compute the figure?

  I  have  exchanged   e-mails with a prominent group member, but he
  was engaged in other matters and not interested at the time.

 Thanks and regards
--
jjartus