SLIME TRAIL

Copyright (c) 1992 Bill Taylor

The game starts at an empty nxn rhombus board, say 10x10,  with the following setup (Green player starts):

 
  • GOAL CELL - The board obtuse corners are the goal cells (one for each player).
  • MOVE - A player, at each turn, moves the white stone into an empty adjacent cell. After the move, the player also drops a black stone into the cell where the white stone was. 
    • However, it is illegal to go to a cell from which it becomes impossible to reach any home cell. (It is valid if only one can be reached.).
  • GOAL - That player wins whose goal cell is entered (regardless of who moves it). If the  White stone becomes impossible to move in a non-goal cell, it is a tie.
 
An example

If it is Red to move, he can play at g11 and Green has no good move to answer. If g10 then h11, h10, i11, ... and if h11 then i12

If it is Green to move, and if he plays g11, then the same move sequence is not longer good for Red.

Here is a sample game for a smaller board.

A game of Slime Trail

Green starts (marked stone) 

Moves: e nw e nw ne nw ne! nw w sw se w sw e se w t se w sw e sw e se e

Red resigns 1-0. Green wins.

The board shows the final position. 

Slime trail can also played on a square grid. Here is a game played on a 8x8 chess board.

A game of Square Slime Trail

Green starts (marked stone) 

Moves: sw e sw e e ne e n nw w s e sw se sw se w w n w nw nw n nw ne nw s ne e s e sw! [any other move would be a win for the Green!]  

Green resigns 0-1, Red wins

The board shows the final position. 

A variant by Bill Taylor and Richard Rognlie, in 2004, is called Medusa. Players decide how many heads (whites stones) are to be played. Initially, there's one head on the center of a 8x8 board. Then, on his turn, each player picks a head on board and orthogonally or diagonally slides over a sequence of empty cells (placing black stones during its path). If the number of heads still didn't reach the maximum, the player leaves a head at the initial moving cell.

Here are some initial moves from a Medusa(3) match:

MEDUSA(3)
======
a b c d e f g h i ___B____J_
. . . . . . . . . 1. h2   h8
. . . . . . . x . 2. hb8  
. . . . . . o o . 3.
. . . . . o . o . 4.
. . . . x . . o . 5.
. . . . . . . o . 6.
. . . . . . . o . 7.
. x o o o o o o . 8.
. . . . . . . . . 9.


a b c d e f g h i ___B____J_
x . . . . . . . . 1. h2   h8
. o x o o o o o . 2. hb8  bd5
. . o . . . o o . 3. a1   c2
. . . o . o . o . 4. dg6
. . . . o . . o . 5.
. . . o o o x o . 6.
. . o . . . . o . 7.
. o o o o o o o . 8.
. . . . . . . . . 9.


a b c d e f g h i ___B____J_
o o o o o o o x . 1. h2   h8
. o o o o o o o . 2. hb8  bd5
. . o o . . o o . 3. a1   c2
. . . o o o x o . 4. dg6  cf5
. . . . o o o o . 5. fg5  g4
. . . o o o x o . 6. h1
. . o . . . . o . 7.
. o o o o o o o . 8.
. . . . . . . . . 9.

The entire match:

a b c d e f g h i ___B_____J_      _B_____J_
o o o o o o o o o 1. h2    h8   11. a2    d7
o o o o o o o o o 2. hb8   bd5  12. c4    c6
o o o o . . o o o 3. a1    c2   13. c4b5  bd5
o . o o o o x o o 4. dg6   cf5  14. resigns, 0-1
o o o x o o o o o 5. fg5   g4
o . x o o o o o o 6. h1    i1
o . o o o o o o o 7. i8    i9
o o o o o o o o o 8. b9    a9
o o o o o o o o o 9. g7    e7
                  10 a8    a3

The hexagonal variant is called Hydra, and follows the same rules. Here's a sample game using four heads:

HYDRA(4)
========
abcdefghijklmnopq ___J____B_
    o o o o x     1. i5   l2
   o o x . o o    2. if2  m9
  o . o . o . o   3. mq5  f8
 x . . o o . . o  4. fc5  a5
o o . . o . . . o 5. qm1  lk1
 o o . o o . . o  6. d8   ke1
  o o o . o . o   7. b4   h2
   x o . . o o    8. resigns, 0-1 (all positions have NIM value zero)
    . . . . o     9.

In Slime-Moku, after each move, the slime leaves alternating color stones. A player wins if he makes a 5 in-a-row with his stones (if no player are able to do that, after the board is full, the game is a tie). Also, if before the board is full, the Slime cannot move (all adjacent cells are occupied), the next player may move the Slime to any other empty cell.

Another variant for 3 players is called Snake Pit is played on the next hexagonal board. Each player has 4 stones (snakes) that can move. On each turn, each player moves 3 of the 4 snakes to an empty adjacent cell (PIE rule: in the 1st and 2nd move, the players only move 1 and 2 snakes). A player loses when he can no longer make his legal move, i.e. when he has TWO snakes totally blocked.

I found at the Spanish Snark Magazine #5 an entry that is very similar to Slimetrail which seems an independent design. It's called Tesoro (Treasure): the first player marks the top-right cell, and then each player moves from there, marking the previous as visited. The first to enter the bottom-left cell (the treasure) wins the game:

A variant that appeared in a Dutch game server, c.2008, is called Penguins. Each cell has a value that the player gets by moving there. Then, the cell became unused. The original game has four penguins and a random setup of numbers.

Here's one fixed setup, where player drop their own penguin (so, here penguins are not shared):

     1 1 1 2 1 1              - - - = - -      
    1 1 2 1 1 1 1            - - = - - - -     
   2 1 1 1 3 1 2 1          = - - - # - = -    
  1 1 3 1 1 1 1 1 2        - - # - - - - - =   
 1 2 1 1 1 2 1 3 1 1      - = - - - = - # - -  
1 1 1 1 2 1 1 1 1 1 1    - - - - = - - - - - - 
 1 1 3 1 1 2 1 1 2 1      - - # - - = - - = -  
  2 1 1 1 1 1 3 1 1        = - - - - - # - -   
   1 2 1 3 1 1 1 2          - = - # - - - =    
    1 1 1 1 2 1 1            - - - - = - -     alternative view:
     1 1 2 1 1 1              - - = - - -      -=# means 123 cell values    

João Neto and Bill Taylor proposed, in 2009, the following variant:

  • 12* move series.

  • The first three moves on each side are to place a penguin on a 1-point cell.

  • After that, the penguins move queenwise, and are not allowed to land on or pass over any other penguin or blank cell.

  • When a penguin moves it leaves the cell behind blank (eaten).

  • Whenever a penguin is placed or moves to a numbered cell, the player scores that many points (fish).

  • If a player can no longer move, his opponent keeps moving until he also can no longer move.

  • Most fish wins.

A sample match:

abcdefghijklmnopqrstu         __Bill________Joao___
     - - - = - -           1. ----   j5     h9   q6
    - - = - - - -          2.  h7    n7     h3 q6p5
   = -   b   -   -         3. j5l3 n7o8   h9j9 h3g4
  - -   -   j - - =        4. h7f7 o8m10  g4i6 j9l7
 - = - -     b j - -       5. f7g6 m10n9  i6j7 l7p3
- b -     - - -     -      6. g6c6 n9r9   j7l5 p3s6
 - -           - j -       7. r9q8 l3k4   s6r7 l5m4
  = - - - - -     -        8. k4j3 q8n5   resign
   - =     -   -           9.
    - - - -   - -         10.
     - - = - - -          11. 

Carlos Santos proposed, in 2007, Chesstrail:

Like Slimetrail but with three pieces (each player only moves one per turn) each piece moves differently: one as a chess bishop, one as a knight and one as a rook.

Orouborus is a 2008 variant by João Pedro Neto:

  • Players take turns moving both ends of the slime-worm, each to some adjacent cell.

  • After each move, each end leaves a stone of that player's colour.

  • The worm may not move onto a coloured cell.

  • If at some point before the board is full, a worm-end cannot move normally, the next player who is able to must split the other end into two heads.

  • A player wins if he makes a 3 in-a-row with his stones.

  • If both ends become blocked simultaneously, the next player to move wins.

Here's a sample match:

João starts  nw.e  

      . . . . .
     . . . . . .
    . . . . . . .
   . . . J . . . .
  . . . . b J . . . 
   . . . . . . . . 
    . . . . . . . 
     . . . . . .
      . . . . .
  
João starts  nw.e  w.se  w.ne ne.e   e.sw  nw.se
              w.w sw.sw sw.w  se.w  se.ne   e.w  & wins

       . . . . .
      j b . . . .
     b b j . . . .
    j j b j . . . .
   . b . . b j j b .
    . J B . . b j .
     . . B J . j b
      . . b j b .
       . . . . .  

Caduceus is a 2009 variant by Bill Taylor:

  • Played on an 8x8 board, each player starts with two stones, at opposite corners.

  • Group-restricted 12* moves per turn.

  • On each move, a player removes the tail of his group and adds two successive rookwise-adjacent new stones on empty cells at the head of it.

  • After the 2nd move the extremes may not become adjacent.

  • A player loses if he cannot complete a legal turn.

Here are some matches:

                     _Bill_    _Joao_ 
. . . . . . . .   1. ws  --    ee  wn
. . j . b . . .   2. ww  nn    ss  ww 
. . j . b . . .   3. se  nn    se  nn
. . j J b b . .   4. es  en  1-0
. . . B J B . .   5.
. b b b j . . .   6. 
. . . . j j . .   7.
. . . . . . . .   8.


                     _Joao_    _Bill_
. b-b-b-b j j j   1. es  --    sw  ee 
. b-b-b b j . j   2. se  nw    ss  en
. j-j-j B J . j   3. es  wn    ww  nw
. j-j j-j . . j   4. sw  ne    nn  wn
b . . . j j . .   5. nw  en    ww  ws
b . . . . J B .   6. ne  nn    ww  se
b-b b b b b b .   7. es  nn    ee  en
. . . . . . . .   8. es  ww    ee  ee  
                  9. es  ss    ss  en  0-1


                     _Bill_    _Joao_ 
b_b_b . . j-j-j   1. --  es    ws  ne    
b . , j . J j-j   2. ee  nn    sw  ee 
b J . j-j-j-j .   3. ss  ww    wn  ee 
b j-j b_b , . .   4. ww  ne    en  ee
b j-j b b_b b b   5. nn  en    ww  sw
b j-j b_b . . b   6. en  ww    ss  ww
b_b j-j-j . . b   7. ww  ww    ee  nw
. b_b_B j-j . B   8. ss  ss    en  wn
                  9. ss  en    ne  wn 
                 10. ss  ee    nw  en
                 11. es  es    wn  wn
                 12. ss  ee     0-1