I just want to add that it is possible to identify the unique odd ball out of 13 ones.

Ilya Novikov

On Mon, 30 Dec 1996, Mark Covello wrote:

> > Problem > > > > >>>You Have 12 balls. > > >>>Identical to the eye > > >>>11 balls have identical weights > > >>>1 ball is either heavier or lighter > > >>>You have a balance scale > > >>>You can take 3 measures > > >>>How can you identify the odd ball > > >>> > > > I'm sorry; I know I should ignore this post, but > I just can't. Here goes for the glory of SAS-L > and to show that we watch more Columbo than SPSS > byteheads: > > Split balls into 3 groups of 4 each call them > A1-A4 > B1-B4 > C1-C4 > > Weigh 1: A1-A4 vs B1-B4 > balance: > ===> bad ball is in C1-C4 > weigh 2: C1, C2 vs A1,A2 > balance: > ====> bad ball is C3 or C4 > weigh 3: C3 vs A1 > Balance: > bad ball is C4 > Not Balance: > Bad Ball is C3 > weigh 2: C1, C2 vs A1,A2 > Not balance: > ====> bad ball is C1 or C2 > weigh 3: C1 vs A1 > Balance: > bad ball is C2 > Not Balance: > Bad Ball is C1 > > That takes care of alloutcomes in which the first weighing > is in balance > > Next suppose: > Weigh 1: A1-A4 vs B1-B4 > Not balance: > ======> bad ball is in A1-A4,B1-B4 > Note direction of imbalance(for sake of explanation > say A1-A4 is heavier than B1-B4, but the argument > works equally as well in the other direction) > Weigh 2: A1,A2,A3,B1 vs C1-C3,A4 > Not Balance in same direction (ie A1,A2,A3,B1 is heavier): > =====> bad Ball is in A1, A2, A3 AND bad ball is heavier > Weigh 3: A1 vs A2 > Balance: > ====> bad ball is A3 > Otherwise > Bad ball is heavier of A1, A2 > Not Balance in other direction (ie A1,A2,A3,B1 is lighter): > =====> bad ball is in B1(lighter), A4(heavier) > Weigh 3: B1 vs C1 > Balance: > bad ball is A4 > Otherwise > Bad ball is B1 > > > The remaining cases all occur when weigh 2 ends in balance: > > Weigh 2: A1,A2,A3,B1 vs C1-C3,A4 > Balance: > =====> bad ball is in B2, B3, B4 and bad ball is lighter > Weigh 3: B2 vs B3 > Balance: > =====> B4 is bad > Not balance: > =====> the lighter ball of B2, B3 is bad > > > I think that covers all possible outcomes. > > I hope someone gets extra credit for this. I solved > this in a graduate Probability course about 10 years > ago and I still took about 1/2 hour to come up with the answer > now. > > > > -- > ******************************************************** > Mark S. Covello > Programming Consultant > current assigment: > Barra > Berkeley, California > > The views expressed in this post do not necessarily > represent the views of Barra. > > "At the end we preferred to travel all night, > Sleeping in snatches, > With the voices singing in our ears, saying > That this was all folly." > > T. S. Eliot > << The Journey of the Magi >> > > ******************************************************** >