Sally's Journal
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02:07 pm
[Link]  Yay, pancakes!
Tina, Laura, me, and assorted other mathmos (about 12 of us in total) had a lovely lunch sat round eating pancakes and proving that mathmos can be sociable, if only with other mathmos. (The problem of the weighings is still bugging me  12 balls, one of which is either heavier or lighter than the rest. Three weighings, find the ball *and* whether it's heavier or lighter. They narged away on this over lunch, but I was too preoccupied covering myself in golden syrup to see if they ever got a solution.)
In other news, my letter to Rag got a reply, stating that because they had phoned all the pub landlords for permission before collecting, they didn't need a house to house collection license. I'm not sure if they're right or not (any opinions?) but they then demolished their own argument by backing this up with the statement "you don't need a council license to collect on privately owned property like a shopping centre", which I know you do need, as I've just finished organising a grafton centre collection.
I'm tired. And should be doing maths...

 
  From:  emperor 
Date:  February 24th, 2004 02:21 pm (UTC) 

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I think they're talking out of their arse, but you could ask the Council (since if they're right, it'll save you a huge amount of hassle next time you want to do a pub collection).
Love you.  From:  gnimmel 
Date:  February 24th, 2004 02:30 pm (UTC) 

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WRT the balls  I haven't worked it out to the end, but I get the idea that if you divide the balls into three groups of four and weigh one against another (this either finding out that they're equal > the eight you've weighed are the reference weight or else that they're not > the remaining ones are the reference weight and you have four balls which might be heavier and four balls which might be lighter), then divide into three different groups of four and do the same again, then do so a third time, you should be able to get the answer; assuming you've chosen the groups well. There will be an answer on't interweb somewhere, anyhow. Here's a starter for the maths answer. _ SPOILER  1) Weigh abcd vs efgh If they are equal then oddball is one of i,j,k,l 2a) Weigh ij vs ka. If equal, l is oddball, can weigh l against any ball on weighing 3) If ij>ka then 3a) Weigh i vs j: equal=>k lighter i>j => i heavier i [ Error: Irreparable invalid markup ('<j =>') in entry. Owner must fix manually. Raw contents below.] Here's a starter for the maths answer. _
SPOILER
 1) Weigh abcd vs efgh
If they are equal then oddball is one of i,j,k,l
2a) Weigh ij vs ka. If equal, l is oddball, can weigh l against any ball on weighing 3)
If ij>ka then
3a) Weigh i vs j: equal=>k lighter i>j => i heavier i<j => j heavier
If ij<ka then
3b) Weigh i vs j: equal=>k heavier i>j => i lighter i<j => j lighter
Then you just consider the case w.l.o.g abcd>efgh ...  From:  tienelle 
Date:  February 25th, 2004 12:12 am (UTC) 

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Assuming you haven't already worked this out, the trick is to maximize the information gained from each weighing. This is equivalent (proof available, FSVO "proof") to making the probabilities of each possible outcome (left heavier, equal, right heavier) as nearly equal as possible.
You will need to use some balls you know not to be the odd ball to achieve this. Me and Edith sat down and hashed out a solution (same as benparker's, as far as his goes), which I've menat to do for ages.
Observe that there are 27 possible outcomes, and only 24 possible solutions to distinguish between. A little fiddling, and judicious use of balls you know to be of standard weight is then enough to solve it.  From:  teleute 
Date:  February 25th, 2004 06:07 am (UTC) 

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oh God! not another goldensyruponpancakesperson. You must be from up north too, just like Adrian *sigh*. Weirdo ;)
At least you don't call it treacle. What! Golden syrup on pancakes if definitely the nicest way to eat them.... :)  From:  teleute 
Date:  February 26th, 2004 06:49 am (UTC) 

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no no no! It's lemon juice and sugar! Golden syrup is for putting on toast. ;)  From:  atreic 
Date:  February 26th, 2004 04:50 pm (UTC) 

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Treacle is the black stuff you make, err, treacle toffee from. Golden syrup is golden. And goes well on *everything*
And for all I claim I'm from up north, I'm sure half of LJ are about to claim that Derbyshire is the midlands...  From:  teleute 
Date:  February 27th, 2004 02:13 am (UTC) 

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you *sound* like you're from up north.
Oh, and while I'm talking to you: did the photographer really catch Jeannine pinching your bum at the wedding, or does it just look like that?  From:  atreic 
Date:  February 27th, 2004 01:28 pm (UTC) 

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you *sound* like you're from up north. Says the girl whose family live in Durham, last bleak outpost of collegiate civalisation before Scotland...
I believe Derbyshire's north. Lots of people from Cambridge disagree with me though, so I've kind of given up on the point. A friend was convinced that Manchester was North, but Retford wasn't, until I pointed out that if you drew a straight line across the country from my house he was south of it.
did the photographer really catch Jeannine pinching your bum at the wedding
I really have to see these wedding pictures... go on, you know my broadband can take it :) Although I'd like to think I'd have remembered that... :)  From:  teleute 
Date:  February 28th, 2004 02:26 am (UTC) 

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But my parents only moved to Durham when I was 18. I was born in Yorkshire (making me a northerner, dammit), but I grew up in Oxford, hence the severe lack of nothern accent. As any fule kno, it is the Thames which constitutes the North/South boundary. We've got two solutions here in ixwin's journal.  From:  atreic 
Date:  February 27th, 2004 01:37 pm (UTC) 

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Cheers!
(Err, who are you, and why are you reading this? I don't mind, I'm just nosey...) Just wandered in when ixwin said she'd found the problem in your LJ. As for who I am, an Oxford maths graduate (so I doubt we've met), now living in Bedford and who tends to waste time browsing other peoples LJs when linked (and yours seems reasonably interesting).  From:  atreic 
Date:  February 29th, 2004 11:11 pm (UTC) 

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Oxford, maths... hmmm, you probably know some of the OULES lot then?
(Have friended you as you said my journal was interesting. Have no idea what the logic of that is even in my own brain. Maybe the dull friends only posts will proove you wrong :) Oh, and you're a mathematician, so you must be interesting, right?) hmmm, you probably know some of the OULES lot then?
Not many. Noga's the only one that springs to mind.
Oh, and you're a mathematician, so you must be interesting, right?
I hope so :) Actually, mathematicians IME seem to come in two flavours interesting and dull except on two or three very narrow subjects. Fortunately you don't see many of the latter as tehy tend to spend their time in the Rad Cam (or wherever the Cambridge maths library is).
Have friended you back. 
