My goal is to pot balls A and B into the pockets numbered 1 and 2 in the billiard table below (diagram at left), using the cue ball O with only two strikes in it.

To do this, my first shot is to strike the cue ball to the point "d"; the cue ball mirror-reflects to the point "f" and strikes the ball B, which falls into pocket 1. The cue ball is now in the position of the potted ball B (diagram at right).

Next, to pot ball A, I strike the cue ball to the point "l". The cue ball mirror-reflects to the point "o", strikes the ball A that mirror-reflects in the point "b" and is potted in pocket 2.

         a   b   c   d   e                a   b   c   d   e
     +---+---+---+---+---+---+        +---+---+---+---+---+---+
     |   |   |   |   |   |   |        |   |   |   |   |   |   |
   p +---A---O---+---+---+---+ f    p +---A---+---+---+---+---+ f
     |   |   |   |   |   |   |        |   |   |   |   |   |   |
   o +---+---+---+---B---+---+ g    o +---+---+---+---O---+---+ g
     |   |   |   |   |   |   |        |   |   |   |   |   |   |
   n +---+---+---+---+---+---+ h    n +---+---+---+---+---+---+ h
     |   |   |   |   |   |   |        |   |   |   |   |   |   |
     1---+---+---+---+---+---2        1---+---+---+---+---+---2
         m   l   k   j   i                m   l   k   j   i               

How must you proceed to pot the balls A, B, C, and D, each one in each of the 4 pockets shown (1-2-3-4), with 4 strikes in the cue ball?

                       a   b   c   d   e       
                   1---+---+---+---+---+---2
                   |   |   |   |   |   |   |
                 p +---+---+---A---B---O---+ f 
                   |   |   |   |   |   |   |
                 o +---+---C---+---+---+---+ g
                   |   |   |   |   |   |   |
                 n +---+---+---+---D---+---+ h
                   |   |   |   |   |   |   |
                   +---+---+---3---+---+---4 
                       m   l       j   i     

The balls A, B, C and D may never touch each other, and the order of potting the balls and where is up to you. And, in your shots, you can only strike the cue ball to another ball or to the points marked in the table.

1) 0 -> l -> o -> b -> A
A -> 4

2) 0 -> d -> g -> j -> C
C -> 1

3) 0 -> B
B -> 2

4) 0 -> e -> f -> D
D -> 3

Posted by Praneeth on 2008-06-23 10:49:28