*Number of players:* 2 or more
*Equipment:* 4×4 or larger grid, pebbles or other tokens to mark squares
Set up
Alexandria Jones <http://letsplaymath.wordpress.com/alexandria-jones/>
and her brother Leon played Avoid Three with pebbles on a grid scratched
in the sand, but you can also use pencils or markers on graph paper. You
need a rectangular playing area at least 4×4 squares large. The bigger
your grid, the longer your game.
How to play
* Take turns placing a pebble or dot in one of the grid squares. But
don't let your pebble line up with any two others. If you put the
3rd stone in any straight line — vertical, horizontal, or diagonal
— you lose.
* Beware: many lines are not obvious. For one thing, the pebble
squares do not have to be touching to be in line. Think of a chess
knight moving steadily southeast across the board. The squares
that he would land on form a straight line.
* Also, pebbles do not have to be evenly spaced to make a line. See
the example above for two lines that are quite easy to miss.
* Use a ruler or other straight edge to test any disputed lines. If
you can place the ruler so that it touches the top right corners
of all three squares, those squares are in line (assuming your
grid is reasonably even). Or count off the *slope*: If you move
consistently over-and-up, over-and-up, over-and-up — the same
amount over and the same amount up each time, like a drunken chess
knight who has forgotten his normal move — then the squares you
land on are all in line.
Endgame
* When a player makes a line of three or more pebbles, he is out of
the game. If a line is not noticed before the next person plays,
however, it doesn't count.
* The last player remaining wins the game.
Comments
Avoid Three is a "poison" variation of traditional tic-tac-toe, which
means the situation that would win the normal game instead becomes the
losing move. I don't know who invented the game, but I first encountered
it in Mathematical Activities
<http://astore.amazon.com/letsplaymath-20/detail/0521285186/103-0672877-8960609>
by Brian Bolt, one of my favorite resources for math club activity
ideas. If you host a math club or teach middle-school-or-older students,
I highly recommend any of the books in this series:
