Odds would have to play a part. 11 balls are equal, so weighing 5 and 5 may, with good odds, establishes 10 as equal, leaving only 2 in question. One of those two is either lighter or heavier. Knowing the others are equal it would only take one more weigh-in to establish the odd ball, for a total of 2 weigh-ins. However, it may not work that easily because the odds might be against the first weighing resulting in 10 equal weights.
Eliminating the equal weights as soon as possible reveals the odd ball. What are the odds? But the question being "what is the "Least" number of weighings...." implies excellent odds, therefore it would have to be 2 as it plays out like this; Only two balls are weighed and one side lowers, obviously one ball being the lighter or heavier ball and the other being equal weight to the other 10. One ball is then removed, noting its weight and put off to the side as one of the other ten is placed on the scale. If they balance out then the removed ball is the odd ball and if they don't balance out the ball left on the scale for the second weigh-in is the odd ball and depending on whether or not it lowered or raised determines it heavier of lighter weight among the rest. Answer, with ultimate odds, is 2. On Mar 12, 7:25 am, ornamentalmind <[email protected]> wrote: > By the way, I first found the problem in a Scientific American decades > ago. I solved it in about 45 min. Slow, yes...however, over the years, > I've come up w/3 different possible correct solutions. > > On Mar 11, 9:18 pm, Don Johnson <[email protected]> wrote: > > > Ok, I found it on the net(yes, I cheated.) It seems an offal lot of > > work for ONE less weighing. Did I mention I'm laZy? On a > > cost/benefit analysis I believe my way is better. And I'm stickin' to > > it.;-) > > > Puzzles Smuzzles. *harrumph* > > > dj > > > On Thu, Mar 11, 2010 at 11:08 PM, ornamentalmind > > > <[email protected]> wrote: > > > incorrect > > > > On Mar 11, 9:04 pm, Don Johnson <[email protected]> wrote: > > >> I thought about it again. Actually, you could put half in on scale > > >> and half in another. 1)One would be heavier. So then you split one > > >> side again and weight them.2)If they are even then you know that > > >> different ball didn't come from that side and now you know if the ball > > >> is heavier or lighter. 3)You split the balls(3 each scale) with the > > >> odd ball in them to narrow it down. 4)weigh two of the remaining 3-if > > >> they are even you know the 3rd is your odd ball. If one is(lighter or > > >> heavier based on earlier discovery) you know that one is the oddball. > > > >> So 4 times. > > > >> I think. > > > >> dj > > > >> On Thu, Mar 11, 2010 at 10:56 PM, Don Johnson <[email protected]> wrote: > > >> > Total guess is six but you can stop as soon as the scales aren't equal. > > > >> > dj > > > >> > On Thu, Mar 11, 2010 at 10:53 PM, ornamentalmind > > >> > <[email protected]> wrote: > > >> >> Years ago I proffered this puzzle to ME: > > > >> >> 12 balls…all appear to be identical. One and only one of them is a > > >> >> little heavier OR a little lighter than the rest. > > >> >> You have a balance scale…two pans hanging similar to what the statue > > >> >> of blind justice holds. > > > >> >> Problem: What is the *least* number of weighings necessary to know > > >> >> *for sure* which of the 12 is different *and* whether the specific > > >> >> ball is lighter or heavier than the rest? > > > >> >> On Mar 11, 7:32 pm, Chris Jenkins <[email protected]> wrote: > > >> >>> Indeed...I'd hate to hear you lost your marbles! > > > >> >>> On Thu, Mar 11, 2010 at 10:30 PM, Slip Disc <[email protected]> wrote: > > >> >>> > lmao, I'd be nuts to even consider it. > > > >> >>> > On Mar 11, 9:28 pm, Chris Jenkins <[email protected]> > > >> >>> > wrote: > > >> >>> > > Fortunately it wasn't a botched vasectomy, or you might not have > > >> >>> > > had the > > >> >>> > > balls! > > > >> >>> > > On Thu, Mar 11, 2010 at 10:25 PM, Slip Disc <[email protected]> > > >> >>> > > wrote: > > >> >>> > > > I'm in recovery right now after a botched operation. I had my > > >> >>> > > > gall > > >> >>> > > > bladder removed and the doctor accidentally cut out part of my > > >> >>> > > > stomach. I was beyond upset but when I told him I was going > > >> >>> > > > to file a > > >> >>> > > > lawsuit he said I didn't have the guts. > > > >> >>> > > > On Mar 11, 9:19 pm, Chris Jenkins <[email protected]> > > >> >>> > > > wrote: > > >> >>> > > > > Not that I'm above them... > > > >> >>> > > > > Two maggots were fighting in dead Ernest. > > > >> >>> > > > > Sticks float. They wood. > > > >> >>> > > > > On Thu, Mar 11, 2010 at 10:19 PM, Chris Jenkins > > >> >>> > > > > <[email protected]>wrote: > > > >> >>> > > > > > *dying* > > > >> >>> > > > > > Puns are the worst. > > > >> >>> > > > > > On Thu, Mar 11, 2010 at 10:14 PM, Slip Disc > > >> >>> > > > > > <[email protected]> > > >> >>> > wrote: > > > >> >>> > > > > >> Then of course you should know How Long was the Chinese > > >> >>> > > > > >> man's name > > >> >>> > and > > >> >>> > > > > >> how to make an Egg Roll, right? > > > >> >>> > > > > >> On Mar 11, 8:49 pm, Chris Jenkins > > >> >>> > > > > >> <[email protected]> > > >> >>> > wrote: > > >> >>> > > > > >> > Great fun! I've always been a fan of riddles and puzzle > > >> >>> > > > > >> > games. > > > >> >>> > > > > >> > On Thu, Mar 11, 2010 at 9:44 PM, Slip Disc > > >> >>> > > > > >> > <[email protected]> > > >> >>> > > > wrote: > > >> >>> > > > > >> > > Yeah, I knew the original set would lay waste to the > > >> >>> > complexity, > > >> >>> > > > but > > >> >>> > > > > >> > > it would have on it's own without the correlation > > >> >>> > > > > >> > > proved to be > > >> >>> > > > more > > >> >>> > > > > >> > > perplexing. It was fun at the least. > > > >> >>> > > > > >> > > On Mar 11, 8:39 pm, Chris Jenkins > > >> >>> > > > > >> > > <[email protected] > > > >> >>> > > > wrote: > > >> >>> > > > > >> > > > If you check the time stamps, it took about five > > >> >>> > > > > >> > > > minutes. :D > > >> >>> > The > > >> >>> > > > > >> > > predictable > > >> >>> > > > > >> > > > range of the downward progression led me > > >> >>> > > > > >> > > > immediately to the > > >> >>> > > > > >> correlation > > >> >>> > > > > >> > > with > > >> >>> > > > > >> > > > the original set. Calculus, for the win! > > > >> >>> > > > > >> > > > On Thu, Mar 11, 2010 at 9:35 PM, Slip Disc < > > >> >>> > [email protected]> > > >> >>> > > > > >> wrote: > > >> >>> > > > > >> > > > > Simply smashing ol chap, I'm a bit gobsmacked. > > > >> >>> > > > > >> > > > > How many hours did it take you? hehehe! > > > >> >>> > > > > >> > > > > On Mar 11, 8:03 pm, Chris Jenkins < > > >> >>> > [email protected] > > > >> >>> > > > > >> wrote: > > >> >>> > > > > >> > > > > > I'm still waiting for the response from Slip! He > > >> >>> > apparently > > >> >>> > > > > >> didn't > > >> >>> > > > > >> > > take > > >> >>> > > > > >> > > > > my > > >> >>> > > > > >> > > > > > order, and tonight's overnight rate is > > >> >>> > > > > >> > > > > > increasing > > >> >>> > > > .0345343782%! > > > >> >>> > > > > >> > > > > > On Thu, Mar 11, 2010 at 3:24 AM, archytas < > > >> >>> > > > > >> [email protected]> > > >> >>> > > > > >> > > > > wrote: > > >> >>> > > > > >> > > > > > > Collaterally derivitise that last option > > >> >>> > > > > >> > > > > > > Chris! > > > >> >>> > > > > >> > > > > > > On 11 Mar, 03:17, Chris Jenkins < > > >> >>> > > > [email protected]> > > >> >>> > > > > >> > > wrote: > > >> >>> > > > > >> > > > > > > > Elementary, my dear boy! > > > >> >>> > > > 6.5192024052026487145829715574291844165280937789100654589503 > > > >> >>> > > > > >> > > > > > > > On Wed, Mar 10, 2010 at 7:20 PM, Slip Disc < > > >> >>> > > > > >> [email protected]> > > >> >>> > > > > >> > > wrote: > > >> >>> > > > > >> > > > > > > > > Well Chris, you're really sharp so, what > > >> >>> > > > > >> > > > > > > > > is the > > >> >>> > next > > >> >>> > > > in > > >> >>> > > > > >> this > > >> >>> > > > > >> > > > > sequence? > > > >> >>> > > > > >> > > > > > > > > 20.024984394500785727697212148323, > > > >> >>> > > > > >> > > > > > > > > 13.114877048604001304688219995272, > > > >> >>> > > > > >> > > > > > > > > 9.230384607371460986883556451096, > > > >> >>> > > > > >> > > > > > > > > ?........................................? > > > >> >>> > > > > >> > > > > > > > > Hint: It also has to do with the > > >> >>> > > > > >> > > > > > > > > Universe. > > > >> >>> > > > > >> > > > > > > > > Anyone? > > > >> >>> > > > > >> > > > > > > > > On Mar 10, 8:20 am, Chris Jenkins < > > >> >>> > > > > >> [email protected]> > > >> >>> > > > > >> > > > > wrote: > > >> >>> > > > > >> > > > > > > > > > *laughing* > > > >> >>> > > > > >> > > > > > > > > > Indeed, sir, Douglas Adams is who I was > > >> >>> > referring > > >> >>> > > > to. > > > >> >>> > > > > >> > > > > > > > > > On Wed, Mar 10, 2010 at 8:19 AM, Slip > > >> >>> > > > > >> > > > > > > > > > Disc < > > >> >>> > > > > >> [email protected] > > > >> >>> > > > > >> > > > > wrote: > > >> >>> > > > > >> > > > > > > > > > > Come to think of it, probably that > > >> >>> > > > > >> > > > > > > > > > > was what > > >> >>> > Chris > > >> >>> > > > was > > >> >>> > > > > >> > > referring > > >> >>> > > > > >> > > > > > > too. > > >> >>> > > > > >> > > > > > > > > > > The solar reference threw me off but > > >> >>> > > > > >> > > > > > > > > > > the real > > >> >>> > > > problem > > >> >>> > > > > >> was > > >> >>> > > > > >> > > that > > >> >>> > > > > >> > > > > I > > >> >>> > > > > >> > > > > > > had > > >> >>> > > > > >> > > > > > > > > > > just finished off a six pack of > > >> >>> > > > > >> > > > > > > > > > > Samuel Adams. > > > >> >>> >http://www.samueladams.com/verification/?nocookie > > > >> >>> > > > > >> > > > > > > > > > > Now I'll have that cigar but first > > >> >>> > > > > >> > > > > > > > > > > cut 82.5 > > >> >>> > off > > >> >>> > > > it's > > >> >>> > > > > >> length > > >> >>> > > > > >> > > to > > >> >>> > > > > >> > > > > > > remove > > >> >>> > > > > >> > > > > > > > > > > the bad tasting stuff. > > > >> >>> > > > > >> > > > > > > > > > > On Mar 10, 6:46 am, Lee > > >> >>> > > > > >> > > > > > > > > > > <[email protected]> > > >> >>> > > > wrote: > > >> >>> > > > > >> > > > > > > > > > > > Ahhh and here I was thinking > > >> >>> > > > > >> > > > > > > > > > > > Douglas Adams. > > >> >>> > He > > >> >>> > > > of > > >> >>> > > > > >> the > > >> >>> > > > > >> > > '42' > > >> >>> > > > > >> > > > > > > quote. > > > >> >>> > > > > >> > > > > > > > > > > > On 9 Mar, 22:58, Slip Disc < > > >> >>> > [email protected]> > > >> >>> > > > > >> wrote: > > > >> >>> > > > > >> > > > > > > > > > > > > Adams is a lunar impact crater > > >> >>> > > > > >> > > > > > > > > > > > > that is > > >> >>> > located > > >> >>> > > > in > > >> >>> > > > > >> the > > >> >>> > > > > >> > > > > rugged > > >> >>> > > > > >> > > > > > > > > > > > > southeastern section of the Moon, > > >> >>> > > > > >> > > > > > > > > > > > > near the > > >> >>> > > > lunar > > >> >>> > > > > >> limb. > > >> >>> > > > > >> > > It > > >> >>> > > > > >> > > > > lies > > >> >>> > > > > >> > > > > > > just > > >> >>> > > > > >> > > > > > > > > to > > >> >>> > > > > >> > > > > > > > > > > > > the southwest of the crater > > >> >>> > > > > >> > > > > > > > > > > > > Legendre. > > > >> >>> > > > > >> > > > > > > > > > > > > Adams Latitude 31.9S > > >> >>> > Longitude > > >> >>> > > > 68.2E > > >> >>> > > > > >> > > > > Diameter > > >> >>> > > > > >> > > > > > > (km) > > >> >>> > > > > >> > > > > > > > > > > > > 66.0 > > > >> >>> > > > > >> > >http://www.fourmilab.ch/earthview/lunarform/cratall.html > > > >> >>> > > > > >>http://en.wikipedia.org/wiki/Adams_%28lunar_crater%29 > > > >> >>> > > > > >> > > > > > > > > > > > > On Mar 9, 9:26 am, Lee > > >> >>> > > > > >> > > > > > > > > > > > > <[email protected] > > > >> >>> > > > wrote: > > > >> >>> > > > > >> > > > > > > > > > > > > > Ummm err wot? > > > >> >>> > > > > >> > > > > > > > > > > > > > On 9 Mar, 14:54, Slip Disc < > > >> >>> > > > [email protected]> > > >> >>> > > > > >> wrote: > > > >> >>> > > > > >> > > > > > > > > > > > > > > Its the Lunar Crater, located > > >> >>> > > > > >> > > > > > > > > > > > > > > on the > > >> >>> > Moon, > > >> >>> > > > not > > >> >>> > > > > >> > > Archy's > > >> >>> > > > > >> > > > > > > moon. > > > >> >>> > > > > >> > > > > > > > > > > > > > > On Mar 9, 8:52 am, Lee < > > >> >>> > [email protected] > > ... > > read more » -- You received this message because you are subscribed to the Google Groups ""Minds Eye"" group. 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