X-Virus-Scanned: clean according to Sophos on Logan.com Return-Path: Sender: To: lml@lancaironline.net Date: Tue, 03 Jul 2007 18:54:21 -0400 Message-ID: X-Original-Return-Path: Received: from imo-d21.mx.aol.com ([205.188.144.207] verified) by logan.com (CommuniGate Pro SMTP 5.1.10) with ESMTP id 2156423 for lml@lancaironline.net; Tue, 03 Jul 2007 17:14:18 -0400 Received-SPF: pass receiver=logan.com; client-ip=205.188.144.207; envelope-from=Sky2high@aol.com Received: from Sky2high@aol.com by imo-d21.mx.aol.com (mail_out_v38_r9.2.) id q.c1f.1a3cbdee (32913) for ; Tue, 3 Jul 2007 17:13:32 -0400 (EDT) From: Sky2high@aol.com X-Original-Message-ID: X-Original-Date: Tue, 3 Jul 2007 17:13:32 EDT Subject: Re: [LML] Re: ADAHRS TSO puzzler X-Original-To: lml@lancaironline.net MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="-----------------------------1183497212" X-Mailer: 9.0 Security Edition for Windows sub 5365 X-Spam-Flag: NO -------------------------------1183497212 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit 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 ************************************** See what's free at http://www.aol.com. -------------------------------1183497212 Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: quoted-printable

In a message dated 7/3/2007 2:18:10 P.M. Central Daylight Time,=20 brent@regandesigns.com writes:

<= FONT=20 style=3D"BACKGROUND-COLOR: transparent" face=3DArial color=3D#000000 size= =3D2>You will=20 need some of all the materials and information listed. You have 27 Contine= ntal=20 pistons that appear identical. Twenty six of the pistons weigh 623 grams a= nd=20 one piston weighs 624 grams. The pistons have a specific density of 0.09=20 pounds per cubic inch. You have a five gallon bucket of water, a four lite= r=20 clear plastic container (that will accommodate one piston), a knife, two=20 dimes, a penny, half a roll of duct tape, 3 feet of 0.020" safety wire and= a=20 simple balance beam scale that has a 50 Kg capacity and can indicate a 0.1= =20 gram difference between the items placed on the pans. What is the fe= west=20 number of measurements needed to identify the heavy piston with=20 certainty?

Brent,

Ahh, I had to go get another tool, Occam's razor. Since I was usi= ng a=20 BIG simple balance beam, I knew I had to think clearly. I got myself a beer=20= and=20 contemplated the possibilities. I put the knife, the dimes and penny i= n my=20 left pocket. I used the duct tape to keep my sleeves rolled up and out= of=20 the way. I used the water on my garden and recycled both the metal buc= ket=20 and the plastic container. The safety wire was put to good use since i= t is=20 the same size as the floss I use. I then had another beer. I clo= sed=20 the door to the shed containing the pistons and the balance beam so a gust o= f=20 wind wouldn't confuse anything.

I put 13 pistons on each side of the balance beam and if it balanced, t= he=20 one left out was 624 grams. If not, I would take the heavier= =20 group of thirteen (setting aside the 14 pistons) and put 6 on each side of t= he=20 scale. If it balanced, the one set aside would be the heavie= st=20 at 624 grams. If not, I would take the heavier group of six=20 (Another beer, setting aside the 7 leftovers with the 14) and put 2 on each=20= side=20 of the scale. If it balanced, then the heaviest would be in=20= the=20 group of 2 that I set aside. If not, I would then have a=20 heavier group of 2 to check, adding the discarded 4 to the pile of=20 21. Placing 1 on each side of the scale, the heaviest would be the one= =20 weighing 624 grams and the lighter one would be returned to the=20 stack. I would then have another beer.

But, to answer your original question, it would take as few as one=20 weighing, but no more than 4, to determine the heavy piston.

Grayhawk

See what's f= ree at AOL.com= .

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