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Turnablock

### Rules for the turnablock game

The game is very simple. You and the computer take turns flipping
tokens: black squares turn to white and vice versa. Whoever turns the
whole board to white (the target) first wins.
The only condition is that the lower
right corner of the rectangle must be black (the base).
**Play**: Click on a black piece
then drag to specify your rectangle to flip. Note: the square that you
click will be the lower right corner of your rectangle.
You can change the size of the board from 3x3 to 8x8. You can also select
an easy or hard opponent. Click *restart* to start the game
over.

This game was invented by J. H. Conway, and
was described in the *Mathematical Games* column of Scientific American.
The winning strategy is described there, and is related to the winning
strategy for Nim. The *hard* setting
implements the winning strategy, while the *easy* setting just tries
to avoid making boneheaded moves. You can look at the Java console to
see how you're doing.

A couple interesting points about the game. The player who goes first
(i.e. you) can force a win by playing properly except for boards of
size 3x4, 3x8, 4x7, and 7x8, for which the second player can force a win.
Also, note that the game is guaranteed to
eventually end; you can't flip forever.

The source is here.

You can find web pages with descriptions of more Conway games
here
and a collection of mathematical games links by
Prof. Eppstein and
Jeff Erickson.

You may also be interested in Conway's (surprisingly expensive) book
Winning Ways: For Your Mathematical Plays.

WebCounter:
Ken Shirriff:
shirriff@eng.sun.com
This page:
http://www.righto.com/java/turnablock.html
###### Copyright 2000 Ken Shirriff. Last updated 3/13/2001.
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