| From : Lucifer (lee sung-tak) Date : Sun Aug 9 17:09:58 1992 Subject: Re: 12 ball problem 12 ball problem is most known and very good puzzle. It has many solutions. I will post analytic algorithm here. Solution: (cut out and keep for your handy reference guide) Number the balls 0,1,2,3,4,5,6,7,8,9,a,b (mentally, if necessary) and make the following three weighings: X 0+1+4+6 v. 5+9+a+b Y 0+4+8+a v. 2+5+6+7 Z 3+4+5+9 v. 6+7+8+b. Then consult this table, where L means the left side dropped, R means the right side dropped, and E means the balance balanced (ugh!). X Y Z result X Y Z result X Y Z result L L L 4 is heavy R L L 6 is light E L L 7 is light L L R 5 is light R L R impossible E L R 8 is heavy L L E 0 is heavy R L E a is heavy E L E 2 is light L R L impossible R R L 5 is heavy E R L 8 is light L R R 6 is heavy R R R 4 is light E R R 7 is heavy L R E a is light R R E 0 is light E R E 2 is heavy L E L b is light R E L 9 is heavy E E L 3 is heavy L E R 9 is light R E R b is heavy E E R 3 is light L E E 1 is heavy R E E 1 is light E E E all equal Theoretically, what you have is 27 possible results from 3 weighings, and 24 possible conclusions (12 balls, each of which may be light or heavy). satisfyable?? I have different solutions also. bye.. |