My book does not have a solution. You are right that it takes a while to
write it all out. When I did it back in the 60's I used a tree diagram! Here
is one twig of a branch of the tree.
Weighing 1: weigh 4 against 4. Assume they balance. Call all 8 of these
marbles good. Call the other 5 questionable.
Weighing 2: weigh 3 good marbles against 3 questionable marbles. Assume they
balance. You now have 11 good marbles and 2 questionable.
Weighing 3: weigh 1 good marble against 1 questionable marble. Assume they
balance. The bad marble is now the last questionable one. At this point you
know it is bad but cannot tell if it is heavier or lighter.
The other branches of the tree get much trickier to analyze. I hope your
students have a good time with this problem.
R. S. (Chuck) Tiberio
Mathematics Department
Wellesley High School phone: (781) 446-6290 x230
Wellesley, MA 02481 email: tiberio@tiac.net
Visit me at http://www.tiac.net/users/tiberio