The Factor Game

The Factor Game is a modification of Dr. Factorwhich originally appeared as one part of a four part program called Playing to Learnpublished by HRM.  (A Microworlds 2.0  version of the program is available from CLIME)

The Game

Two players compete for high score by picking numbers (1 to 25) from a screen which are then added to their score. There is a catch though. Whenever Player A picks a number, the total of every factor of that number still showing on the screen is added to the opponentís score. When the opponent, Player B, chooses a number, that number is added to his/her score, but Player A gets the total of all remaining factors of the number B chose. For example, if A chooses 25, then B gets 1 and 5 (since they are factors of 25). At this point A has 25 points and B has 6.  And now it is Bís turn to go. The chosen numbers are removed from the screen.

Variations of the Game

1. Play the game with a different range of numbers. For example, you can play a longer game by typing RANGE 40.

2. Play a game of 10 several times. Does the player going first always win (assuming both players are using the best possible strategy)?
 

To download a version of this game from the Internet, click here.