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From: Leroy Quet on 1 Jul 2010 11:34
Here is a game for two players, and, you guessed it, it uses an n-by-n
grid drawn on paper. (I suggest an n of at least 8.)

First, the players each secretly guess how many squares will be filled
in before the game terminates. Each player writes their guess down and
hides the guess from their opponent.

Next, fill in with a pen/pencil the center square (if n is odd) or one
of the 4 center squares (if n is even).

(*)The players then both secretly choose a direction. Player 1 chooses
either up, vertically-steady, or down. Player 2 chooses either left,
horizontally-steady, or right. The players each write down their
choices.

Then the players both reveal their choices simultaneously.

The next square filled in has the vertical direction chosen by player
1 and the horizontal direction chosen by player 2 from the last square
filled in; and this next square filled in is adjacent (touching on a
side or on a corner) to the last square filled in. (There are 9
possible combinations of directions, including not changing the square
at all {when both players pick steady}.)

If that adjacent square is already filled in, then the game is over.

But if that square is empty before being filled in on the current
move, then the game continues. (Go to *.)

When the game is over, the winner is the player whose guess for the
number of squares filled in is closest to (either greater than or
lesser than or equal to) the actual number of squares filled in.

(By the way, if both players choose the direction 'steady' at the same
time, the game ends then, of course.)

Thanks,
Leroy Quet

From: James Dow Allen on 2 Jul 2010 16:15
On Jul 1, 10:34 pm, Leroy Quet <qqq...(a)mindspring.com> wrote:
> The players each write down their choices.
> Then the players both reveal their choices simultaneously.

Much faster would be for one player to declare via 0,1 or 2 coins
hidden in hand, with the other declaring orally.

If a player declares "right" while the current square is already
at the right edge, is that "right" equivalent to "steady"
or do we wrap around to the far left?

I don't know about the strategy, except that psychology can
play a role. For example, if opponent seldom starts "steady",
I might pick a largish number, then start with "steady" as
first move. Opponent will think I picked smallish number and
will help me win!

James Dow Allen
From: Leroy Quet on 3 Jul 2010 12:32


James Dow Allen wrote:
>...
> If a player declares "right" while the current square is already
> at the right edge, is that "right" equivalent to "steady"
> or do we wrap around to the far left?
>
>...

I should state that if the last square filled in is on the edge of the
grid, then one (or both) player's choices are then limited.

I guess if a player states "right" and the last square filled is on
the right edge of the grid, then that player has violated the rules
and forfeits.
:)

Thanks,
Leroy Quet

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