In a message dated 7/3/2007 2:18:10 P.M. Central Daylight Time,
brent@regandesigns.com writes:
You will
need some of all the materials and information listed. You have 27 Continental
pistons that appear identical. Twenty six of the pistons weigh 623 grams and
one piston weighs 624 grams. The pistons have a specific density of 0.09
pounds per cubic inch. You have a five gallon bucket of water, a four liter
clear plastic container (that will accommodate one piston), a knife, two
dimes, a penny, half a roll of duct tape, 3 feet of 0.020" safety wire and a
simple balance beam scale that has a 50 Kg capacity and can indicate a 0.1
gram difference between the items placed on the pans. What is the fewest
number of measurements needed to identify the heavy piston with
certainty?
Brent,
Ahh, I had to go get another tool, Occam's razor. Since I was using a
BIG simple balance beam, I knew I had to think clearly. I got myself a beer and
contemplated the possibilities. I put the knife, the dimes and penny in my
left pocket. I used the duct tape to keep my sleeves rolled up and out of
the way. I used the water on my garden and recycled both the metal bucket
and the plastic container. The safety wire was put to good use since it is
the same size as the floss I use. I then had another beer. I closed
the door to the shed containing the pistons and the balance beam so a gust of
wind wouldn't confuse anything.
I put 13 pistons on each side of the balance beam and if it balanced, the
one left out was 624 grams. If not, I would take the heavier
group of thirteen (setting aside the 14 pistons) and put 6 on each side of the
scale. If it balanced, the one set aside would be the heaviest
at 624 grams. If not, I would take the heavier group of six
(Another beer, setting aside the 7 leftovers with the 14) and put 2 on each side
of the scale. If it balanced, then the heaviest would be in the
group of 2 that I set aside. If not, I would then have a
heavier group of 2 to check, adding the discarded 4 to the pile of
21. Placing 1 on each side of the scale, the heaviest would be the one
weighing 624 grams and the lighter one would be returned to the
stack. I would then have another beer.
But, to answer your original question, it would take as few as one
weighing, but no more than 4, to determine the heavy piston.
Grayhawk