Will it bounce?
A mathematical billiard table is in the form of a rectangle with integral sides, and just four pockets, one in each corner. A ball shoots out of one pocket at angles of 45° to the sides. Will it bounce round the table for ever, or end up in one of the other pockets?
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It will definitely end up in one of the other three pockets. It is not possible for it to bounce for ever or end up in the pocket it started from.
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