Teaser 1917: Trick shots
From The Sunday Times, 13th June 1999 [link]
Joe’s billiard table is of high quality but slightly oversized. It is 14 ½ feet long by 7 feet wide, with the usual six pockets, one in each corner and one in the middle of each long side.
Joe’s ego is also slightly oversized and he likes to show off with his trick shots. One of the most spectacular is to place a ball at a point equidistant from each of the longer sides and 19 inches from the end nearest to him. He then strikes the ball so that it bounces once off each of the four sides and into the middle pocket on his left.
He has found that he has a choice of directions in which to hit the ball in order the achieve this effect.
(a) How many different directions will work?
(b) How far does the ball travel in each case?
This puzzle is included in the book Brainteasers (2002). The puzzle text above is taken from the book.
[teaser1917]
S2T2 
Jim Randell 9:03 am on 20 October 2020 Permalink |
As with beams of light, it is easier to mirror the table and allow the ball to travel in a straight line. (See: Enigma 1039, Enigma 1532, Teaser 2503).
If we mirror the table along all four sides we get a grid-like pattern of tables and the path of the ball becomes a straight line between the source and the target pocket.
The line must cross each colour side once. So vertically it must cross a green and a red (in some order) before ending up in the pocket. Which means only an upward line will do. Horizontally it must cross an orange and a blue line before hitting the pocket. The two possible paths are indicated in this diagram:
We can then calculate the distances involved. In both cases the vertical distance is 2.5 widths = 210 inches.
And the horizontal distances are: 2.5 lengths − 19 inches = 416 inches, and: 1.5 lengths + 19 inches = 280 inches.
The required distances are then:
Solution: (a) There are 2 directions which will work; (b) In once case the ball travels: 38 feet, 10 inches; in the other case: 29 feet, 2 inches.
The paths of the ball on the table look like this:
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