This is a continuation of the question A balance with three pans, detecting the lightest pan (find the one lighter ball). It was told to me by a friend, Markus Götz, who put it online here: Deviating Ball Puzzles (pdf).
The three-pan balance
Imagine a balance with not two, but three pans. Weightings using the balance follow these rules:
- If there exists a pan that is lighter than each of the other two pans, then this pan goes up and the other two pans go down to a stop. (Note that one cannot see which of the two heavier pans, if any, is the heaviest.)
- If there is no single lightest pan, then nothing happens. (This includes the case of two equally light pans and one heavier pan.)
Let's call this the "lightest-pan-detection-rule" (LPDR).
You are given n balls, one of which is heavier. What is the largest n, so that the heavier ball can be identified with at most k weightings? (k >= 1)
The "normal" balls are all of the same weight. You are to identify the deviating ball by using the balance a maximum number of weighings stated in the puzzle, weighing only the given balls. You are also to present a method to identify the deviating ball.