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## Quiz of the Month (February 2006)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

There are four solutions: 192, 219, 273, 327
Notes.

Intelligent trial and error is not too tedious. (The number must lie between 123 and 329. It can contain no zero and no repeated digit ....)
Alternatively, write a simple computer program.

#### THIS MONTH'S QUIZ

Assume that an English billiard table measures 8 ft by 4 ft, with a pocket at each corner and one at the center of each long side. The baulk line is 2 ft from one of the shorter sides. Ignore the finite size of the balls and assume a ball always moves in straight lines, and when it strikes a cushion it leaves it at the same angle as it strikes, as shown.
A ball is projected from the mid-point of the baulk line, and strikes the cushion BC at X. Find the distance of X from C in each of the following cases:

 1. After striking the cushion BC it then strikes cushion CD and enters the pocket A. 2. After striking the cushion BC it then strikes cushion CD and enters the pocket E. 3. After striking the cushion BC it then strikes cushion CD, then cushion DA, and enters the pocket B.

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