Draft:Bpow1997-16

This week's problem was submitted by Dr Libin Mou of the Bradley University Mathematics Department. T

Original Problem: You have 12 Ping Pong balls. One of them is bad, which means it's either heavier than normal or lighter than normal. You are given a balance scale and are asked to find the bad one. Furthermore, you also need to determine whether it's heavier or lighter. How can you achieve this using the scale only three times?

Generalized Problem: This time, you have <m>(3n - 1)/2 - 1</m> Ping Pong balls and you are allowed to use the scale n times, with n greater than or equal to 1. Notice that when <m>n = 3</m>, <m>(3n - 1)/2 - 1 = 12</m>, which is our original problem.

Problem by Alberto L Delgado, from the now extinct Bradley Problem of the Week.