Re: Puzzle

Duncan Chiu (
Wed, 23 Dec 1998 22:13:36 -0500

That's right, Chuck. You cannot identify the weight of the 13th marble, but you
can if there are 12 marbles.

Does your book show the solutions? It will take me a while to type up the


Chuck Tiberio wrote:

> Duncan,
> 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:
> Visit me at