The thinking is not interesting, it is exact. I take two balls and place them on the scale, let's say X and Y
The scale tips off balance with X weighing in heavier. One of the balls on the scale, either X or Y is the odd ball, either a lighter one or a heavier one than the other 11 balls. Eleven of the balls are of the same weight, therefore one of the balls on the scale is the same weight as the other 11 balls. I remove one of the balls, lets say X the heavier ball, and place it off to the side. I now place "one" of the 10 other balls (B), which are all of equal weight, on the scale which now holds ball Y. The scale balances out with one of the (B) balls and the Y ball indicating that the Y ball is part of the 11 balls that weigh the same. Therefore the X ball is the odd ball and determined to be heavier than the rest. All this in 2 weigh-ins. On Mar 12, 11:09 am, ornamentalmind <[email protected]> wrote: > Slip...'possible situation' does not match knowing 'for sure'...as > interesting as your thinking may be... > > On Mar 12, 8:44 am, Slip Disc <[email protected]> wrote: > > > Forget the odds, still the procedure that I presented IS one > > "possible" situation. It is possible that it would turn out that way > > for me and so I would identify the odd ball with only 2 weigh-ins. > > > On Mar 12, 10:30 am, ornamentalmind <[email protected]> wrote: > > > > Uhhh, odds have nothing to do with it since I clearly said “*for > > > sure*”…in other words, all possible situations must be addressed…not > > > just chance. > > > > On Mar 12, 7:11 am, Slip Disc <[email protected]> wrote: > > > > > 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: > > ... > > read more » -- You received this message because you are subscribed to the Google Groups ""Minds Eye"" group. 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