December 2021
Problem of the Month

Carom Billiard Table

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

Send any comments or questions to: David Pleacher