A 'snooker' table (measuring 8 metres by 4m) with 4 'pockets' (measuring 0.5m and placed at diagonal slants in all 4 corners) contains 10 b***s (each with a diameter of 0.25m) placed at the following coords:

2m,1m...(white ball)...and red b***s...

1m,5m... 2m,5m... 3m,5m

1m,6m... 2m,6m... 3m,6m

1m,7m... 2m,7m... 3m,7m

The white ball is then shot at a particular angle from 0 to 360 degrees (0 being north, and going clockwise).

Just to make it clear, a ball is 'potted' if at least half of the ball is in area of the 'pocket'

Assuming the b***s travel indefinitely (i.e. no loss of energy via friction, air resistance or collisions), answer the following:**a:** What exact angle/s should you choose to ensure that all the b***s are potted the quickest?**b:** What is the minimum amount of contacts the b***s can make with each other before they are all knocked in?**c:** Same as b, except that each ball - just before it is knocked in - must not have hit the white ball on its previous contact (must be a red instead of course).**d:** What proportion of angles will leave the white ball the last on the table to be potted?

Guest May 9, 2014