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#1 2012-10-04 12:29:58

MathsIsFun
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Registered: 2005-01-21
Posts: 7,535

New Puzzles 4


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#2 2012-10-04 19:21:44

bob bundy
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Registered: 2010-06-20
Posts: 6,308

Re: New Puzzles 4

hi

Sorry ... bit of a rush.

Weighty Puzz think I have another soln.

More later

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#3 2012-10-04 20:00:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,512

Re: New Puzzles 4

Hi MIF;

Funny that Bob and I went for the same problem.

For the weighty problem there are 10 solutions to the problem. Not counting permutations. Want to add the rest? Hope I did not prune out any others.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#4 2012-10-05 13:55:05

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: New Puzzles 4

Great! I will put that in the solution.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#5 2012-10-05 21:03:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,512

Re: New Puzzles 4

Hi MIF;

A mathematical solution would be nice but I do not have one.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#6 2012-10-06 04:57:19

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,375

Re: New Puzzles 4

I would think there is one, thought it does seem GFs might be of use.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#7 2012-10-06 08:29:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,512

Re: New Puzzles 4

Hi anonimnystefy;

GF's usually count the number of solutions not the type of solutions. For that, I usually call on number theory.

Still in all a gf played an important part in the program. Without it there would be no program.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#8 2013-03-04 00:04:21

Thurhame
Member
Registered: 2013-03-03
Posts: 6

Re: New Puzzles 4

There is a problem with the "Three Of The Best" puzzle.
The puzzle claims there are two solutions to "1+(1/(1+(1/...)))". However, it actually converges to the golden ratio

, meaning there is only one solution.

MORE COMPLEX PROOF:
The formula is the limit as n goes to infinity of the sequence

defined by
.
Assume some
exists (otherwise the sequence would be undefined).
Define a sequence
.
We proceed by induction.
Base step:

Inductive Hypothesis:


Thus we have proved by induction the relation
for all
.
Since
is a sequence of the form
, this ratio converges to the golden ratio.

Last edited by Thurhame (2013-03-05 13:28:02)

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#9 2013-03-04 00:15:36

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,891
Website

Re: New Puzzles 4

Wonderful, Thanks!


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#10 2013-03-04 02:39:19

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,375

Re: New Puzzles 4

Hi Thurhame

Can you specify where it was claimed that 1+1/(1+1/(1+...)) is equal to 2?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#11 2013-03-04 04:24:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,512

Re: New Puzzles 4

Hi;

The answer given is 2 when it should be the golden ratio.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#12 2013-03-04 05:23:07

Thurhame
Member
Registered: 2013-03-03
Posts: 6

Re: New Puzzles 4

anonimnystefy wrote:

Hi Thurhame

Can you specify where it was claimed that 1+1/(1+1/(1+...)) is equal to 2?

Oh, my mistake, it just said there were two solutions to the formula. However, that's still wrong; my proof shows that any solution must be equal to the golden ratio, i.e. there are at most 1 solutions.

Edited my post above. Thanks!

Last edited by Thurhame (2013-03-04 05:26:01)

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#13 2013-03-04 06:30:13

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,375

Re: New Puzzles 4

Hi Thurhame

Yes, with that I agree. The answer should be one. I think they didn't consider that the number must be positive.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#14 2013-03-05 13:27:40

Thurhame
Member
Registered: 2013-03-03
Posts: 6

Re: New Puzzles 4

Ah, thanks for reminding me, my simple less-rigorous proof isn't adequate if i'm only proving the number of solutions, rather than the value. Removing it now. Hope the more complex proof doesn't make anyone's eyes glaze over.

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