Non Specification Billiard Ball

Coding

G= Known Good

U = Unknown (Could be heavy or light)

H= Possibly Heavy - (but can not be light)

L = Possibly Light - (but can not be heavy)

Initially we have 12 U -- 12 unknown balls.

Balance 1 is 4 Balls versus 4 Balls UUUU Vrs UUUU

Case 1 - scales balance - we have 8 good balls and 4 unknown - 8G4U

Case 2 - Scales do not balance In this case we know the 4 balls not used are good, the side of the scales that went down may contain a heavy ball or the side that went up may contain a light ball. The fact balls may be Heavy or Light but not the opposite is important. Hence 4G4H4L

Now we look at case 1 untill conclusion We have 8G4U

Balance 2 GGG Vrs UUU Scale balances we now have 11 good ball, and one which is unknown - 11G1U

    Balance 3 is a simple to find out if 1 unknown ball is heavy or light.

     Scale does not Balance   - UUU goes up  - one of the three unknown must be light

     We now have  9G3L

    Balance 3 is   L vrs L    side that goes up is light ball, or if balance ball not used is light

     Scale does not Balance -  UUU goes down - one of the 3  unknown must be heavy     

     We now have  9G3H

    Balance 3 is   H vrs H    side that goes down  is a heavy  ball, or if balance ball not used is heavy

Now we look at case 2 untill conclusion We have 4G4H4L

Balance 2

HHHLL Vrs HGGGG

      Scale balances  - all the balls weighed are good so we are left with 2 possible light balls.  - 10G2L

       Balance 3 is  L vrs L   to show which ball is light

      HHHLL goes up /HGGGG goes down   either the two L s are light or the H from the other side is heavy

     Balance 3 is  L vrs L  to show which is light - or if balances the H not weighed  is a heavy ball.

      HHHLL goes down/HGGG goes up   -  one of the three H's must be heavy.

                           Balance 3  is H vrs H  to show which ball is heavy  - or if it balances the H not wieghed is heavy.

3 Balances is all that is required.

by using divide and conquer technique