This problem rang a very familiar bell with me. After a little research, I
found it.
Suppose you are given 13 objects, 12 of which are the same, but one is
either heavier or lighter than the others. Show that, with 3 weighings using
a pan balance, it is possible to identify the odd object.
This appears in my 1962 edition of Kemeny, Schleifer, Snell, and Thompson's
book "Finite Mathematics with Business Applications" as problem 14 on page
89. I seem to remember solving this problem for some guy on my dorm floor
back in the 60's!! The catch in using 13 marbles instead of 12 is that at
the end of the process you can identify the marble but cannot tell whether
it is heavier or lighter.
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