Does your book show the solutions? It will take me a while to type up the
solutions.
duncan
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: tiberio@tiac.net
>
> Visit me at http://www.tiac.net/users/tiberio