When you rent a table at a pool hall, the proprietor gives you a 4-by-4 tray of 16 balls, as shown
in Figure (a) below. One of these balls, called the “cue ball”, is white, and the remaining 15 are
numbered 1 through 15. At the beginning of a game, the numbered balls are racked up in a
triangle (without the cue ball), as shown in Figure (b).