On Sat, 08 Feb 2003 10:25:08 +0800,

From The Telegraph, UK
8 February 2003

Odd ball letter starts maths puzzle mania
By Robert Uhlig

It started with a 76-word letter from a reader in Gravesend in Kent.
By teatime yesterday, The Telegraph had received its biggest mailbag
in living memory and our telephones were still ringing off the hook.

What elicited such a remarkable response? Not the threat of war in
Iraq, the prospect of top up fees, the plight of transsexuals or
threats to the Tory leadership, but an arcane 17th century
mathematical puzzle concerning a dozen balls.

"Many years ago, a maths lecturer put to me the following question,"
wrote Harold Hopwood, describing a conversation he had over lunch on a
riverboat cruise along the Danube several decades ago.

Mr Hopwood, who has read the Telegraph and completed the crossword
every day since he moved into digs in Leeds in 1937, went on to
describe the conundrum over which he and various members of his family
have lost many nights sleep.

"You have 12 seemingly identical balls, but one of them is odd, in
that it is lighter or heavier than the others," Mr Hopwood wrote.

"Using a pair of scales, determine in three weighings, which ball is
the odd one and whether it is lighter or heavier.

"Now, aged 82, I have still not solved it. Can any kind reader help me
before it is too late?" The challenge had been thrown down and our
readers responded in force.

The letters desk alone received 362 letters and calls - mostly seeking
the answer rather than offering the solution. Other departments were
similarly inundated.

Some of Britain's best mathematical and puzzle-breaking minds stepped
up to the task. Ian Stewart, professor of mathematics at Warwick
University, devised one solution, printed today.

"This is one of the classic puzzles," Prof Stewart said. "It works
because it's wonderfully subtle, very elegant and quite intriguing.
That's probably why so many people took it up."

It is the unknown factor of whether the odd ball is heavier or lighter
than the rest that makes it more difficult than at first it might
seem.

Martin Golubitsky, professor of mathematics at Houston University in
Texas, who worked with Prof Stewart on the solution on the letters
page, said the puzzle had so inspired him as a teenager, he decided to
become a mathematician.

"I was completely enthralled by it at the age of 14 and it took me
several days to solve it," he said.

"This time, it took about 15 minutes, but I'll always have a soft spot
in my heart for it."

According to Prof Stewart, with three weighings allowed and three sets
of four balls to play with, several solutions are possible.

"There are 24 possible answers - one of which says I am the odd ball,"
he said. "But there are three cubed (3x3x3) or 27 possible questions,
so with more questions than answers there's some redundancy and room
for there to be more than one solution."

By lunchtime, Alan Gilliland, our graphics editor, aided by our
cartoonist, Matt Pritchett, had come up with their own solution.

The Gilliland-Pritchett method relies on splitting the balls into
three groups of four and weighing two of them.

If they balance, then one of the third group is the odd ball, and the
right column will weed it out.

If the first weighing does not balance, then the third group can be
discounted, and the sequence shown in the left column will spot the
odd ball.

For Mr Hopwood it was "a great relief" to have the solution at last.

"It is quite wonderful to know after so many years," he said
yesterday.

"I went so far as to try and trace the man I met on the riverboat, but
the cruise company had no record of him."

Any readers who worked it out for themselves should certainly pat
themselves on the back: the dozen ball conundrum is a common
undergraduate maths problem, used to teach communication coding theory
and experimental designs for plant breeding.

http://www.telegraph.co.uk

"Tarzan" wrote in message
...
On Sat, 08 Feb 2003 10:25:08 +0800,

Relevance to gardening was....?

--
Tumbleweed

Remove my socks before replying (but no email reply necessary to newsgroups)

On Sat, 8 Feb 2003 22:52:42 -0000, "Tumbleweed"
wrote:

"Tarzan" wrote in message
.. .
On Sat, 08 Feb 2003 10:25:08 +0800,

Relevance to gardening was....?

The poster lives in a tree.
--
Stuart Baldwin
news\at/boxatrix\dot/co\dot/uk

"Tumbleweed" wrote in message
...
"Tarzan" wrote in message
...
On Sat, 08 Feb 2003 10:25:08 +0800,

Relevance to gardening was....?


The last paragraph I guess. I haven't a clue what it means though:

the dozen ball conundrum is a common
undergraduate maths problem, used to teach communication coding theory
and experimental designs for plant breeding.

Martin