Below is a $8 \enspace \text{ft} \times 4 \enspace \text{ft}$ $\enspace (=243.84 \enspace \text{cm} \times 121.92 \enspace \text{cm})$ billiard table, with a perfectly flat playing surface. The cushions are removed for the sake of simplicity.
You have:
- 16 standard, $2 \frac{1}{4}$-inch $(=5.715 \enspace \text{cm})$ pool balls of the same weight (including the cue ball).
- A mighty cue stick.
You can place the balls anywhere on the table (except the pockets), but all sixteen of them must be used. Then you will have one shot.
I think you already know what your goal is.
In a single shot, you have to pocket all of the balls except the cue ball.
The cue ball itself must never go down a pocket, not even after the others are pocketed.
Technical details
The balls:
- Have a perfect spherical shape.
- Never convert kinetic energy into anything else.
- Collide with one another and the rails in a perfectly elastic manner. (See? No need for cushions.)
- Collide frictionlessly (they don't start spinning when their collision is not head-on).
Parameters for the table:
- The pockets have the exact same size as the balls, but a ball can fall into a pocket by getting even partially above the hole.
- The edge of the playing area goes through the center of each pocket.
Another important notice:
You have to provide a mathematically accurate explanation why your solution works.
It's not enough to present some random arrangement and claim that it is correct “because it works in Universe Sandbox 2”, or whatever simulator you prefer.
Scoring
This puzzle shouldn't take much time to solve, so let's make it a popularity contest. The accepted answer will be the one with the highest number of votes (up minus down) after a week.
You can use a brute force algorithm to solve this puzzle if you want, but I can't even imagine how you could possibly write one.