PUZZLE 3 and tetrahedral, but that’s trivial. The next tetrahedron is a triangle of 3 balls with 1 ball on top, or 4 altogether. But 4 balls won’t make a triangle.” “Ten will,” said Jones. “It makes a triangle with rows of 1, 2, 3, and 4. And it also makes a tetrahedron. Every tet rahedral number is the sum of consecutive triangles; and triangles 1, 3, and 6 add to 10.” Jones took out his calculator. “Let’s see. If I remember my number theory, triangular numbers have the form % n(n + 1) where n is any positive integer. Tetrahedral numbers have the form ^6 n(n + 1) (n + 2).” It didn’t take Jones long to discover that the third number to fit both formulas was between 100 and 200. He could find no other solution less than 200, so this was the number he wanted. With the aid of a pocket calculator, how quickly can you determine the number of balls (not counting the cue ball) used in space pool?
7