This question involves the game \"paper pool\". There are four pockets, one in e

Question

This question involves the game "paper pool".

There are four pockets, one in each corner - A, B, C, D, of a table, made up of so many rows and columns.

Ball is hit on a 45 degree angle starting at corner pocket A. The ball bounces off the sides of the table at 45 degree angles until it goes into a pocket.

Tables are named row by column - eg a 3 by 5 table has 3 rows and 5 columns.

Each time the ball travels, it is called a path. Eg the 3 by 5 table has 7 paths to get into a pocket, and it ends up in pocket c.

The question is:

Some tables have the same answer - ie the 2 by 3 table, the 4 by 6 table and the 6 by 9 table all have the answer 4B.

i) what is the reason they have the same answer?

ii) Name 3 other tables that would have the same answer as a 2 by 3 table.

I'm guessing for part i) they have the same answer as each table is the same multiple as the one before, but I'm not sure if that is the correct technical answer.

Thanks

Explanation / Answer

you are right,

the no.of bounces wont change but the length of path travelled would change.

ii)

8 by12

10 by15

12 by18 would have the same answer as a 2 by 3 table

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