If a ball is hit from the corner of a Carom Billiard Table at a 45° angle,
and if the ratio of the sides
is p:q (expressed in reduced form),
Then determine a formula for the number of times the ball
rebounds before reaching a corner
(answer should be in terms of p and q).
Note: A carom billiard table has no pockets.
Solution to the Problem:
The formula for the number of times a ball rebounds before reaching a corner is P + Q - 2.Try some examples and then try to generalize.
| Table | Reduced (P x Q) | # of rebounds |
|---|---|---|
| 1 x 2 | 1 x 2 | 1 |
| 4 x 8 | 1 x 2 | 1 |
| 4 x 7 | 4 x 7 | 9 |
| 2 x 3 | 2 x 3 | 3 |
| 3 x 5 | 3 x 5 | 6 |
| 4 x 6 | 2 x 3 | 3 |
| 4 x 4 | 1 x 1 | 0 |
Colin Bowey gets extra credit for writing a Logo program that allowed the user to put in any dimensions for the table and it displayed the path of the billiard ball.
Click here to download the table that he compiled showing all table sizes to 102 x 105 with the number of rebounds.
Click here to download an interactive table showing the path of the ball.
Correctly solved by:
| 1. Veena Mg | Bangalore, Karnataka, India |
| 2. Mohamed Sheriff (MEDDORA) | Freetown, Western Area Urban District, Sierra Leone, West Africa |
| 3. Ashley Martin |
Mountain View High School, Mountain View, Wyoming |
| 4. Cash Henrie |
Mountain View High School, Mountain View, Wyoming |
| 5. Tyler Duarte | Central High School, Grand Junction, Colorado |
| 6. Colin (Yowie) Bowey | Beechworth, Victoria, Australia |
| 7. Sapna Dominic and Ivy Joseph | Pune, Maharashtra, India |
| 8. Kelly Stubblefield | Mobile, Alabama |