Sunday Express Skeleton 24Th November...
Crosswords2 mins ago
Pool Pockets
2 Answers
If you only have 4 corner pockets and you have a ball set at a 45 degree angle how many bounces off the sides will it take to go into a corner pocket and why?
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I'm not sure I fully understand the question, but here's some thoughts...
A pool table is normally twice as long as it is wide. You divide the table up into a series of squares which fill the table with twice as many squares along the length as the width. The ball will in general traverse the diagonals of the small squares.
A shot started from a corner pocket at 45 degrees will hit the middle of the far long side and bounce across to the corner pocket on the same long side as the start point (1 bounce).
For every other cushion starting point not at a corner, due to the symmetry of the table, the path taken by the ball ends up bouncing off 6 cushions (not counting the start point but counting the last) until it repeats its path again, so if hit infinitely hard it will bounce of an infinite number of cushions.
Starting at any point in the middle of the table will be equivalent to one of the above paths (ie. if the start is on one of the diagonals of the two large squares making the pool table area it will reach a corner pocket after one or zero bounces, otherwise it will never reach a pocket).
Am I missing something in the question, as there does not seem to be a single answer?
A pool table is normally twice as long as it is wide. You divide the table up into a series of squares which fill the table with twice as many squares along the length as the width. The ball will in general traverse the diagonals of the small squares.
A shot started from a corner pocket at 45 degrees will hit the middle of the far long side and bounce across to the corner pocket on the same long side as the start point (1 bounce).
For every other cushion starting point not at a corner, due to the symmetry of the table, the path taken by the ball ends up bouncing off 6 cushions (not counting the start point but counting the last) until it repeats its path again, so if hit infinitely hard it will bounce of an infinite number of cushions.
Starting at any point in the middle of the table will be equivalent to one of the above paths (ie. if the start is on one of the diagonals of the two large squares making the pool table area it will reach a corner pocket after one or zero bounces, otherwise it will never reach a pocket).
Am I missing something in the question, as there does not seem to be a single answer?
1 to 2 of 2
