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.