TACTIX  by Russ Yost, 15 October, 1990

     Tactix is a "take-away" game similar to NIM.  It was invented by
Piet Hein, a mathematician in Copenhagen, in the '40's.  Martin Gardner
described it in articles in Scientific American in the 50's, and in his
book, The Scientific American Book of Mathematical Puzzles and
Diversions, published by Simon and Schuster, New York, in 1959.

     The game starts with a 6x6 board filled with pieces.  Each player
takes away a group of contiguous pieces from a row or column.  The
object is to force your opponent, in this case, the computer, to take
the last piece.

     Make your play by "dragging" the mouse over the group you wish to
play, starting at one end and continuing to the other.  By "dragging"
is meant: use the mouse to place the cursor on the piece at one end of
the group you wish to remove; depress and then hold down the left mouse
button while moving the cursor with the mouse till it is on the end
piece of the group you wish to remove; release the left mouse button.

     This process selects the pieces to play and they are then
highlighted.  If you wish to change your play at this time, you may
repeat the dragging process; the new play is then highlighted.

     To actually remove the highlighted pieces, "click on" the "PLAY"
box. (Place the cursor in the PLAY box, then depress and release the
left mouse button.)

	If you make an illegal play, it will be rejected and you will be
permitted to try again.

	The computer will then evaluate the results of the plays it can
make, select one, highlight it briefly, then remove the pieces and wait
for you to play again.

	On your turn, you may click on the RESIGN box; a new game will be
started.  Or, you can click on the QUIT box, which ends the session of
game playing.  The scores are not retained for a future session.  You
may alternately quit by clicking on the close gadget in the upper left
corner of the screen.

     Tactix was written in JForth and is "cloned" for public release.

                        PLAY STRATEGY

     This game is related to NIM, a take-away game that starts with a
number of piles of counters, and players may take any number of
counters from any one pile, the object being to take the last piece. 
The pieces in Tactix can be considered to be in a varying number of
groups and the play rules mean that pieces can be removed from only one
group.  However, in contrast to NIM, pieces can be removed such that
the number of groups increases.  When the maximum number of pieces in
any group is two, Tactix becomes strictly a game of NIM, since the
number of groups can not then be increased.  As a result, I think a
helpful strategy is to apply the NIM strategy: play so that the
exclusive-or bit-wise sum of the numbers of pieces in each group is
zero.  Such a board situation is said to be "safe" for the player who
attains it.  For example, suppose there are three groups left
containing 1, 2, and 3 pieces.  These are binary 001, 010, and 011. 
Exclusive or-ing these results in zero.  In NIM this would be a safe
situation, but in Tactix, it may potentially be unsafe, since the group
of three can be split into two groups of one.

     Another modification from NIM, in which the object is to take the
last piece, is required because here the object is to force your
opponent to take the last piece.  Near the end of a game, try to leave
an odd number of groups each containing one piece; this will force the
computer to take the last piece.

     By applying this strategy and using your superior intellect, you
will be able to beat the computer; it is not very smart!

     HAVE FUN!