Its about the puzzle Arch, not about physical attributes. On Mar 12, 6:47 pm, archytas <[email protected]> wrote: > I have no doubt we can isolate the most different (lightest) ball > Slip; but no two balls are actually the same, just approximately so. > > On 12 Mar, 23:07, Slip Disc <[email protected]> wrote: > > > 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 > > ... > > read more »
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