Here is a dumb game (which might help kids learn multiplications and

divisions and about primes, etc.):

2 players.

2 decks of cards, n cards each, the cards in both decks labeled with

the integers from 1 to n (one integer per card).

You also have an m-by-m grid, where m, I suggest, is in the vicinity

of

just over n^(3/2)/2, but m is up to the players.

Players take turns drawing 2 cards, one card from each deck.

Players, after drawing the cards, take the product, k, of the 2 cards'

values.

Players fill in any previously unfilled grid-squares so as to form a

rectangle of area k.

(And the width/height of the rectangle need not be the same as the

cards' numbers, unless 1 and a prime {or another 1} are drawn.)

Players do not have to fill any rectangles if they volutarily skip

their turn or if no rectangle of area k can be filled.

Play continues until either the grid is filled completely or until the

cards have all been drawn, whichever comes first.

3 variations on how to determine winner:

1) Winner has most number of grid-squares filled with their color at

game's end.

2) Winner has most number of rectangles at game's end filled with

their color.

3) Winner is last player to fill in a rectangle.

And, if you want to, maybe you can simply use a standard card-deck

instead.

And you draw 2 cards at a time, assigning appropriate numerical values

to Jack, Queen, King, and Ace, of course.

But how would each winner-determination variation affect strategy?

And what would you suggest for an m based on n?

thanks,

Leroy Quet

## Thursday, September 18, 2008

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