I was surprised that there was only one right answer.  Brent's question was carefully written - What is the fewest number of measurements that will identify the heavy piston WITH CERTAINTY".  Answer is three.  Put two groups of 9 (1/3 of the total) on the beam - if they are the same weight, the heavy one is in the remaining 9.  If the weight is different it is on that group, so now you know that it is in 1/3 of the total.  Divide the 9 into 3rds and do it again to narrow it down to a group of 3.  One more time and you have it, so the answer is 3 and all you need is the balance beam, none of the other stuff.  I got it wrong once in a test, so now I remember it.  The initial number of parts has to be an exponential of 3 to work.  This time it was 3^3.  3^4 samples would take 4 tests, etc.
Gary