A question for math and science people

[mathking]

Pool uses 15 balls (7 solids, 7 stripes and the 8 ball). They are arranged in a triangle.

There is no ideal angle and force. The system is too sensitive to changes in the initial conditions. A minor change in the surface of the pool table or a millimeter change in the position of one ball can greatly change the "correct" angle of incidence. So the correct answer requires statistical mechanics and has a variey of solutions. In general, a firm strike which is a few degrees off of head on the lead ball is the "best" option.

As for minimum force to sink all 15 balls, again there is not one best answer. The minimum force to maximize your chance of sinking all of the balls is likely to be whatever force won't shatter the queue ball and the first ball it strikes. To sink all of the balls, they would have to be bouncing around a LONG time. It is such an unlikely event that it would be essentially impossible to do a real statistical mechanics study. You would not experience success often enough to get any decent conclusions.