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**bruxism** A man designs a 2m by 2m billiard table with only 4 pockets, one in each corner, marked A, B, C, D. A ball is shot from directly in front of one pocket at a 45 degree angle. Obviously, because the billiard table is square, it will go into the diagonally opposite hole.

What happens now if the table is increased to 2 * 3, 2 * 4 , 2 * 5 etc. and the ball is again hit at a 45 degree angle. Is there a way to predict what pocket the ball will go into in each trial?

What about for a table 3 * 3, 3 * 4 3 * 5 etc. Can you predict what pocket it will go in?

Is there a way to write a generalised formula for this, to find out which pocket it will go into for a very large table, 342 * 275 for example?