Subtraction Game

In the Subtraction Game you are given a number of minuends and a number of subtrahends. Players take turns subtracting subtrahends from minuends - one subtraction at a time. Only non negative results are legal. The player unable to move loses. A horizontal line separates minuends (placed above the line in a rectangular array) from subtrahends (always located in a row below the line).

To perform a move, select a minuend and then click on a subtrahends.

The game has three parameters. #Nums is the number (from 1 through 12) of minuends to subtract from. #Subs is the number (from 1 through 8) of possible subtrahends to be subtracted from minuends. Max is the absolute maximum of minuends. Subtrahends may change between 1 and 9 (inclusive). They may be modified when the Define button is checked.

The numbers that could be modified (#Nums, #Subs, Max and subtrahends) are modifed by clicking a little off their vertical central line. Clicking on the right from the line increases the number, clicking on the left decreases it.

When subtrahends form a sequence of consecutive numbers starting with one, the game is equivalent to Scoring. Since the players are free to define subtrahends to their liking, Subtraction Game is more general.

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.

What if applet does not run?

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