May 2, 2007

A multiplication game

This game is focused for young people when learning multiplication.
Let's consider multiplications x*y with values ranging from 1 to 9.

First, one player picks one pair, say x1*y1. The second player chooses another pair x2*y2. Then the second player takes the modulus of the difference , i.e., |x1*y1 - x2*y2| and takes that difference as his points. Then, the second player must choose a pair x2*y3 or x3*y2 (i.e., he must keep one of the numbers from his last picked pair). This is the first turn. Then this is repeated (now the first player starts choosing a pair, makes the difference and choose a related pair, and so on...). Pairs can never be choosed twice.

The game ends when one player cannot continue (there are no similar pairs to choose since all were selected already). The player with less points wins the game.

It's possible to speed things up but restricting to pairs x*y where x<y.

An initial example:

____ Player1 ____________ Player2 ____
--- (--------) 3x5 | 4x4 (1 points) 4x9 --> |3x5-4x4|=1
6x6 (0 points) 6x9 | 7x8 (2 points) 7x9
8x8 (1 points) 8x9 | 9x9 (9 points) 5x9
6x7 (3 points) 6x8 | 7x7 (1 points) 5x7
4x8 (3 points) 5x8 (and so on...)

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