Players:   Two — "ODD" and "EVEN". ODD takes the odd turns (1, 3, 5, etc.); EVEN takes the even (2, 4, 6, etc.)

Equipment:   Pencil and paper

To start:   Make a 4 x 6 grid. One player (decided randomly) writes an X on any square of the grid. The other decides whether to be ODD or EVEN.

Goal:   EVEN wins if, at the end of the game, there are six or more Tic-Tac-Toes on the board. Otherwise, ODD wins. A Tic-Tac-Toe consists of exactly three consecutive Xs or three consecutive Os in a row, column, or diagonal. If a row, column, or diagonal contains four or more consecutive squares with the same symbol, it does not contain a Tic-Tac-Toe. A symbol may be part of two or more Tic-Tac-Toes going in different directions, so it is possible to complete two, three, or even four Tic-Tac-Toes in a single move.

To play:   On your turn, you may write an X or an O on any empty square.

Ending the game   The game is over when all the squares have been filled in.

SIX-TAC-TOE is an “underdog” game because the two players’ chances of winning are almost certainly not equal; one player, the so-called underdog, has a disadvantage, even though it may be very slight. But which player (EVEN or ODD) has the advantage? How big is it? We don’t know, so we’re asking for your help.

• CHALLENGE #1:
  Demonstrate which player has an advantage (or that neither does).

• CHALLENGE #2:
  Demonstrate how much of an advantage EVEN or ODD has.

• CHALLENGE #3:
  Figure out a way to “level the playing field,” that is, to guarantee that both EVEN and ODD have the same chance of winning a single game.

Kadon will award a prize to the best answers received by January 1, 2008. Send your answers to: