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Take-Away Games

Like One Pile, the Take-Away games are played on a single pile of objects. On the first move a player is allowed to remove any number of objects, but the whole pile. On any subsequent move, a player is allowed to remove any number of objects bounded from above by a quantity that depends on the previous move.

The applet below implements three such games. In one, a player can remove no more than what his or her opponent removed on the previous move. In the second game, the condition changes to less than twice of the previous move. An in the third, it's no more than twice the previous move.

<hr> <h3> This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet. </h3> <hr>

Some theory

Copyright © 1996-2008 Alexander Bogomolny