No, it is not. Here's an information theory approach: by asking three questions which have three possible answers each (left side goes down, right side goes down, or equal), there are only 3**3 == 27 possible "inputs". Suppose there were 15 balls --- then there would be 15 * 2 == 30 (each ball can be heavier or lighter than the rest) possible "outputs". There are more outputs than inputs, so it is impossible. (This is the same approach as analyzing the "game tree".)

In fact, this argument shows that it is not possible to do the same for more than 13 balls; a slightly more sophisticated argument shows that 12 is actually the maximum. The best that is possible for 13 balls is determining which ball is different, but not necessarily whether it is heavier or lighter; this is not possible for 14 or more balls.

In reply to Re^2: Odd Ball Challenge by kaif
in thread Odd Ball Challenge by Limbic~Region

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